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enHypothesis Testing: Suppose that you're working for Hotstar. In the past month, the subscription for their product 'Hotstar Premium' has increased a lot.
https://programsbuzz.com/interview-question/hypothesis-testing-suppose-youre-working-hotstar-past-month-subscription-their
<span>Hypothesis Testing: Suppose that you're working for Hotstar. In the past month, the subscription for their product 'Hotstar Premium' has increased a lot.</span>
<span><span lang="" about="https://programsbuzz.com/user/1" typeof="schema:Person" property="schema:name" datatype="" xml:lang="">tgoswami</span></span>
<span>Sun, 01/17/2021 - 22:49</span>
<div class="field field--name-body field--type-text-with-summary field--label-hidden field__item"><p>Suppose that you're working for Hotstar. In the past month, the subscription for their product 'Hotstar Premium' has increased a lot. The analysts in the company claim that the subscription increased mainly due to the premiere of Game of Thrones which is going to happen soon. However, some of them believe that this might not be the sole reason because then people would buy it just 1 or 2 days before the premiere. So there might also be some other reason for the spiked membership. The lead business analyst in your company then claims that at least 60% of the past month subscriptions are due to the premiere of 'Game of Thrones'. </p>
<p>To test this claim you send a survey to some of the users who have purchased the membership in the past month to which 121 users replied. The data for the same has been provided in the Excel <a href="https://programsbuzz.com/sites/default/files/datascience/Hotstar%2BData.xlsx">here</a>. A '1' in column two indicates that they bought the subscription because of 'Game of Thrones' and 0 indicates that they bought it for other reasons. Based on the data answer the following questions.</p>
<p>[Note: You need to use the sample standard deviation instead of the population standard deviation to compute the necessary test-statistic in this case]</p>
<p><strong>Q1: Suppose that the null and alternate hypothesis that you framed in this case are:</strong></p>
<p><strong>H0: Percentage of users who bought the subscription for Game of Thrones ≥ 60%<br />
HA: Percentage of users who bought the subscription for Game of Thrones < 60%</strong></p>
<p><strong>Calculate the approximate value of Z-score using the data as the first step to evaluate your hypothesis.</strong></p>
<ul><li>1.89</li>
<li>-1.89</li>
<li>1.76</li>
<li><strong>-1.76</strong></li>
</ul><p>You first need to calculate the mean and SD of the relevant column 'Why did you purchase Hotstar Premium?' in Excel. If you notice, the mean gives the percentage of users who purchased it because of Game of Thrones. The mean and standard deviation come out to be 0.52 and 0.501 respectively. . Now, you can easily calculate the Z-value as:</p>
<p>Z-value = ¯X−μS/√n=0.52−0.60.501/√121≈−1.76</p>
<p><strong>Q2: From the Z-value you calculated in the last case, what will the p-value be? On the basis of this p-value, what decision will you take for a significance level of 5%?</strong></p>
<ul><li><strong>p-value = 0.0392, Reject the null hypothesis</strong></li>
<li>p-value = 0.0392, Fail to reject the null hypothesis</li>
<li>p-value = 0.2296, Reject the null hypothesis</li>
<li>p-value = 0.2296, Fail to reject the null hypothesis</li>
</ul><p>From the Z-table, the value at -1.76 comes out to be 0.0392. Since this is a left-tailed hypothesis test, this value itself is the p-value. Since, 0.0392 is less than the significance level defined, i.e., 0.05, you reject the null hypothesis.</p>
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Sun, 17 Jan 2021 21:49:18 +0000tgoswami888 at https://programsbuzz.comHypothesis Testing: Suppose that you're working for an education company and you're launching a new course on your website.
https://programsbuzz.com/interview-question/hypothesis-testing-suppose-youre-working-education-company-and-youre-launching
<span>Hypothesis Testing: Suppose that you're working for an education company and you're launching a new course on your website.</span>
<span><span lang="" about="https://programsbuzz.com/user/1" typeof="schema:Person" property="schema:name" datatype="" xml:lang="">tgoswami</span></span>
<span>Sun, 01/17/2021 - 22:38</span>
<div class="field field--name-body field--type-text-with-summary field--label-hidden field__item"><p>Suppose that you're working for an education company and you're launching a new course on your website. For this course, since you want the number of students to be more, you are looking to launch a scholarship program wherein the students who can't afford the course can avail some scholarship after giving an entrance test.</p>
<p>From the past scholarships offered by the company, your CFO claims that the students who pass the test and eventually buy the course get a scholarship of at least 60% on an average. You are a business analyst in the same company and you want to test this claim. So you randomly selected a small sample of 81 students who passed the test and had bought the course and were offered scholarships between 30 - 90%. Here you found that among these 81 students, the average scholarship offered was 57.5% with a standard deviation of 19%.</p>
<p><strong>Q1: What will be the null hypothesis in this case?</strong></p>
<ul><li>H0: Students who passed the test and bought the course get a scholarship of 60% on an average.</li>
<li>H0: Students who passed the test and bought the course get a scholarship of 60% or less on an average.</li>
<li>H0: Students who did not pass the test and bought the course get a scholarship of 60% or less on an average.</li>
<li><strong>H0: Students who passed the test and bought the course get a scholarship of 60% or more on an average.</strong></li>
</ul><p>Recall that the CFO had claimed that the students who passed the test and bought the course get a scholarship of 60% or more on an average. Since this is the claim that you're testing, it becomes your null hypothesis.</p>
<p><strong>Q2: Recall that for the sample of 81 students, the mean scholarship was 57.5% with a standard deviation of 19%. Based on the hypothesis that you framed, what will the decision that you take be?</strong></p>
<p><strong>Choose a 1% significance level.</strong></p>
<ul><li>Reject the null hypothesis.</li>
<li><strong>Fail to reject the null hypothesis.</strong></li>
<li>Insufficient data to make a decision</li>
</ul><p>From the given hypothesis you can calculate that it is a left-tailed test.Now based on the given data, the Z-value would be -</p>
<p>Z=X−μS/√n=57.5−6019/√81≈−1.18</p>
<p>When you look up the Z-table, you'll find that the probability for this Z-value comes out to be approximately 0.119. This is also the p-value that we want. Since this value is greater than the significance level that we defined as 0.01 at the start, we fail to reject the null hypothesis.</p>
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Sun, 17 Jan 2021 21:38:10 +0000tgoswami887 at https://programsbuzz.comTypes of Errors: A screening test for a serious but curable disease is similar to hypothesis testing.
https://programsbuzz.com/interview-question/types-errors-screening-test-serious-curable-disease-similar-hypothesis-testing
<span>Types of Errors: A screening test for a serious but curable disease is similar to hypothesis testing.</span>
<span><span lang="" about="https://programsbuzz.com/user/1" typeof="schema:Person" property="schema:name" datatype="" xml:lang="">tgoswami</span></span>
<span>Sun, 01/17/2021 - 17:14</span>
<div class="field field--name-body field--type-text-with-summary field--label-hidden field__item"><p>A screening test for a serious but curable disease is similar to hypothesis testing. In this instance, the null hypothesis would be that the person does not have the disease, and the alternative hypothesis would be that the person has the disease. If the null hypothesis is rejected, it means that the disease is detected and treatment will be provided to the particular patient. Otherwise, it will not. Assuming that the treatment does not have serious side effects, in this scenario, it is better to increase the probability of ___.</p>
<ul><li>Making a type-I error, i.e., not provide treatment when it is needed.</li>
<li><strong>Making a type-I error, i.e., provide treatment when it is not needed.</strong></li>
<li>Making a type-II error, i.e., not provide treatment when it is needed.</li>
<li>Making a type-II error, i.e., provide treatment when it is not needed.</li>
</ul><p>Here, a type-I error would be providing treatment on false detection of the disease, when, in fact, the person does not have the disease. And a type-II error would be not providing treatment upon failing to detect the disease, when, in fact, the person has the disease. Since the treatment has no serious side effects, a type-I error poses a lower health risk than a type-II error, as not providing treatment to a person who actually has the disease would increase his/her health risk.</p>
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Sun, 17 Jan 2021 16:14:56 +0000tgoswami886 at https://programsbuzz.comTypes of Errors: Consider the null hypothesis that a process produces no more than the maximum permissible rate of defective items.
https://programsbuzz.com/interview-question/types-errors-consider-null-hypothesis-process-produces-no-more-maximum
<span>Types of Errors: Consider the null hypothesis that a process produces no more than the maximum permissible rate of defective items. </span>
<span><span lang="" about="https://programsbuzz.com/user/1" typeof="schema:Person" property="schema:name" datatype="" xml:lang="">tgoswami</span></span>
<span>Sun, 01/17/2021 - 17:09</span>
<div class="field field--name-body field--type-text-with-summary field--label-hidden field__item"><ul><li>To conclude that the process does not produce more than the maximum permissible rate of defective items when it actually does not.</li>
<li>To conclude that the process produces more than the maximum permissible rate of defective items when it actually does.</li>
<li>To conclude that the process produces more than the maximum permissible rate of defective items when it actually does not.</li>
<li><strong>To conclude that the process does not produce more than the maximum permissible rate of defective items when it actually does.</strong></li>
</ul><p>A type-II error refers to not rejecting an incorrect null hypothesis. So, a type-II error would signify that the null hypothesis is actually incorrect, i.e., the process actually produces more than the maximum permissible rate of defective items, but you fail to reject it. In other words, you think that it does not produce more than the maximum permissible rate of defective items.</p>
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Sun, 17 Jan 2021 16:09:55 +0000tgoswami885 at https://programsbuzz.comThe p-Value Method: Suppose you are conducting a hypothesis test where the sample size is 49.
https://programsbuzz.com/interview-question/p-value-method-suppose-you-are-conducting-hypothesis-test-where-sample-size-49
<span>The p-Value Method: Suppose you are conducting a hypothesis test where the sample size is 49.</span>
<span><span lang="" about="https://programsbuzz.com/user/1" typeof="schema:Person" property="schema:name" datatype="" xml:lang="">tgoswami</span></span>
<span>Sun, 01/17/2021 - 17:05</span>
<div class="field field--name-body field--type-text-with-summary field--label-hidden field__item"><p><strong>Suppose you are conducting a hypothesis test where the sample size is 49. Now, you want to conduct another hypothesis test on a different sample, where the sample size is 121. The p-value calculated in the first case comes out to be 0.0512. What will happen to the p-value in the second case if you observe the same values for the sample mean and the sample standard deviation for both the cases?</strong></p>
<ul><li>It will increase.</li>
<li><strong>It will decrease.</strong></li>
<li>It will stay the same.</li>
<li>Cannot be determined.</li>
</ul><p>With an increase in the sample size, the denominator of the Z-score decreases, and thus, the absolute value of Z-score increases, which means that the sample mean would move away from the central tendency towards the tails. This means that the p-value would actually decrease. Conceptually, increasing the sample size will make the distribution of the sample means narrower, and chances of the sample mean falling in the critical region increase. So, the p-value will decrease.</p>
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Sun, 17 Jan 2021 16:05:25 +0000tgoswami884 at https://programsbuzz.comHypothesis Testing: Errors in Hypothesis Testing
https://programsbuzz.com/interview-question/hypothesis-testing-errors-hypothesis-testing
<span>Hypothesis Testing: Errors in Hypothesis Testing</span>
<span><span lang="" about="https://programsbuzz.com/user/1" typeof="schema:Person" property="schema:name" datatype="" xml:lang="">tgoswami</span></span>
<span>Sun, 01/17/2021 - 16:13</span>
<div class="field field--name-body field--type-text-with-summary field--label-hidden field__item"><p><strong>Q1: Mark all the correct options below.</strong></p>
<ul><li>A type-I error occurs when a true null hypothesis is rejected.</li>
<li>A type-I error occurs when the null hypothesis is not rejected when it is, in fact, incorrect.</li>
<li>A type-II error occurs when the null hypothesis is rejected when it is, in fact, correct.</li>
<li>A type II error occurs when the null hypothesis is not rejected when it is, in fact, incorrect.</li>
</ul><p><strong>Q2: Suppose the null hypothesis is that a particular new process is as good as or better than the old one. A type-I error would conclude that ___.</strong></p>
<ul><li>The old process is as good as or better than the new one when, in fact, it is not.</li>
<li>The old process is better than the new one when it really is so.</li>
<li>The old process is better than the new one when, in fact, it is not.</li>
<li>The new process is as good as or better than the new one when it really is so.</li>
</ul><p>A type-I error refers to incorrectly rejecting a true null hypothesis. So, a type-1 error means that the null hypothesis is true, i.e., the new process is as good as or better than the old one, but you reject it, i.e., you conclude that the old process is better.</p>
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Sun, 17 Jan 2021 15:13:10 +0000tgoswami883 at https://programsbuzz.comNull and Alternative Hypotheses: A nationwide survey claimed that the unemployment rate of a country is at least 8%. However, the government claimed that the survey was wrong and the unemployment rate is less than that.
https://programsbuzz.com/interview-question/null-and-alternative-hypotheses-nationwide-survey-claimed-unemployment-rate
<span>Null and Alternative Hypotheses: A nationwide survey claimed that the unemployment rate of a country is at least 8%. However, the government claimed that the survey was wrong and the unemployment rate is less than that. </span>
<span><span lang="" about="https://programsbuzz.com/user/1" typeof="schema:Person" property="schema:name" datatype="" xml:lang="">tgoswami</span></span>
<span>Sun, 01/17/2021 - 15:55</span>
<div class="field field--name-body field--type-text-with-summary field--label-hidden field__item"><p><strong>Problem: </strong>A nationwide survey claimed that the unemployment rate of a country is at least 8%. However, the government claimed that the survey was wrong and the unemployment rate is less than that. The government asked about 36 people, and the unemployment rate came out to be 7%. The population standard deviation is 3%.</p>
<p><strong>Q1: What are the null and alternative hypotheses in this case?</strong></p>
<ul><li><strong><label for="3380432">H0:μ≥8% and H1:μ<8%</label></strong></li>
<li><label for="3380433">H0:μ≤8% and H1:μ>8%</label></li>
<li>H0:μ>8% and H1:μ≤8%</li>
<li>None of the above</li>
</ul><p><strong>Q2: Based on the information above, conduct a hypothesis test at a 5% significance level using the p-value method. What is the Z-score of the sample mean point ¯x= 7%?</strong></p>
<ul><li>-0.2</li>
<li>2.0</li>
<li>-2.0</li>
<li><strong>0.2</strong></li>
</ul><p>μ=8%;σ=3%;n=36;¯x=7%;S.E.=3√36=0.5. Now, Z¯x=7−80.5=−2</p>
<p><strong>Q3: Calculate the p-value from the cumulative probability for the given Z-score using the Z-table. In other words, find out the p-value for the Z-score of -2.0 (corresponding to the sample mean of 7%).</strong></p>
<ul><li>0.9772</li>
<li><strong>0.0228</strong></li>
<li>0.5199</li>
<li>0.4801</li>
</ul><p>The p-value corresponding to a Z-score of -2.0 is 0.0228.</p>
<p><strong>Q4: Make the decision on the basis of the p-value with respect to the given value of α (significance value).</strong></p>
<ul><li><strong>You reject the null hypothesis because the p-value is less than 0.05.</strong></li>
<li>You fail to reject the null hypothesis because the p-value is less than 0.05.</li>
<li>You reject the null hypothesis because the p-value is more than 0.05.</li>
<li>You fail to reject the null hypothesis because the p-value is more than 0.05.</li>
</ul><p>Since the p-value of the Z-score of the sample mean is less than the given p-value of 0.05, we reject the null hypothesis H0:μ≥8%.</p>
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Sun, 17 Jan 2021 14:55:05 +0000tgoswami882 at https://programsbuzz.comThe p-Value Method: Let’s say you work at a pharmaceutical company that manufactures an antipyretic drug in tablet form, with paracetamol as the active ingredient.
https://programsbuzz.com/interview-question/p-value-method-lets-say-you-work-pharmaceutical-company-manufactures-antipyretic
<span>The p-Value Method: Let’s say you work at a pharmaceutical company that manufactures an antipyretic drug in tablet form, with paracetamol as the active ingredient.</span>
<span><span lang="" about="https://programsbuzz.com/user/1" typeof="schema:Person" property="schema:name" datatype="" xml:lang="">tgoswami</span></span>
<span>Sun, 01/17/2021 - 15:47</span>
<div class="field field--name-body field--type-text-with-summary field--label-hidden field__item"><p>Let’s say you work at a pharmaceutical company that manufactures an antipyretic drug in tablet form, with paracetamol as the active ingredient. An antipyretic drug reduces fever. The amount of paracetamol deemed safe by the drug regulatory authorities is 500 mg. If the value of paracetamol is too low, it will make the drug ineffective and become a quality issue for your company. On the other hand, a value that is too high would become a serious regulatory issue.</p>
<p>There are 10 identical manufacturing lines in the pharma plant, each of which produces approximately 10,000 tablets per hour.</p>
<p>Your task is to take a few samples, measure the amount of paracetamol in them, and test the hypothesis that the manufacturing process is running successfully, i.e., the paracetamol content is within regulation. You have the time and resources to take about 900 sample tablets and measure the paracetamol content in each.</p>
<p>Upon sampling 900 tablets, you get an average content of 510 mg with a standard deviation of 110. What does the test suggest if you set the significance level at 5%? Should you be happy with the manufacturing process, or should you ask the production team to alter the process? Is it a regulatory alarm or a quality issue?</p>
<p>Solve the following questions in order to find the answers to the questions stated above.</p>
<p>One thing you can notice here is that the standard deviation of the sample of 900 is given as 110 instead of the population standard deviation. In such a case, you can assume the population standard deviation to be the same as the sample standard deviation, which is 110 in this case.</p>
<p><strong>Q1: Calculate the Z-score for the sample mean (x) = 510 mg.</strong></p>
<ul><li>36.67</li>
<li>-36.67</li>
<li>-2.73</li>
<li><strong>2.73</strong></li>
</ul><p>You can calculate the Z-score for the sample mean of 510 mg using the formula: (¯x - μ) / (σ /√N). This gives you (510 - 500)/(110/√900) = (10)/(110/30) = 2.73. Notice that since the sample mean lies on the right side of the hypothesised mean of 500 mg, the Z-score comes out to be positive.</p>
<p><strong>Q2: Find out the p-value for the Z-score of 2.73 (corresponding to the sample mean of 510 mg).</strong></p>
<ul><li>0.0032</li>
<li><strong>0.0064</strong></li>
<li>0.9968</li>
<li>1.9936</li>
</ul><p>The value in the Z-table corresponding to 2.7 on the vertical axis and 0.03 on the horizontal axis is 0.9968. Since the sample mean is on the right side of the distribution and this is a two-tailed test (because we want to test whether the value of the paracetamol is too low or too high), the p-value would be 2 * (1 - 0.9968) = 2 * 0.0032 = 0.0064.</p>
<p><strong>Q3: Based on this hypothesis test, what decision would you make about the manufacturing process?</strong></p>
<ul><li>The manufacturing process is completely fine and need not be changed.</li>
<li>The manufacturing process is not fine, and changes need to be made.</li>
</ul><p>Here, the p-value comes out to be 0.0064. Here, the p-value is less than the significance level (0.0064 < 0.05) and a smaller p-value gives you greater evidence against the null hypothesis. So, you reject the null hypothesis that the average amount of paracetamol in medicines is 500 mg. So, this is a regulatory alarm for the company, and the manufacturing process needs to change.</p>
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Sun, 17 Jan 2021 14:47:23 +0000tgoswami881 at https://programsbuzz.comp-value method: You are working as a data analyst at an auditing firm. A manufacturer claims that the average life of its product is 36 months.
https://programsbuzz.com/interview-question/p-value-method-you-are-working-data-analyst-auditing-firm-manufacturer-claims
<span>p-value method: You are working as a data analyst at an auditing firm. A manufacturer claims that the average life of its product is 36 months. </span>
<span><span lang="" about="https://programsbuzz.com/user/1" typeof="schema:Person" property="schema:name" datatype="" xml:lang="">tgoswami</span></span>
<span>Sun, 01/17/2021 - 11:21</span>
<div class="field field--name-body field--type-text-with-summary field--label-hidden field__item"><p dir="ltr">You are working as a data analyst at an auditing firm. A manufacturer claims that the average life of its product is 36 months. An auditor selects a sample of 49 units of the product and calculates the average life to be 34.5 months. The population standard deviation is 4 months. Test the manufacturer’s claim at a 3% significance level using the p-value method.</p>
<p>First, <strong>formulate the hypotheses</strong> for this two-tailed test, which would be:</p>
<p dir="ltr"> H₀: μ = 36 months and H₁: μ ≠ 36 months</p>
<p>Now, you need to follow the three steps to <strong>find the p-value and make a decision</strong>.</p>
<p>Try out the three-step process by answering the following questions.</p>
<p><strong>Step 1: Calculate the value of the z-score for the sample mean point of the distribution. Calculate the z-score for the sample mean (¯x) = 34.5 months.</strong></p>
<ul><li>0.86</li>
<li>-0.86</li>
<li>2.62</li>
<li><strong>-2.62</strong></li>
</ul><p>You can calculate the z-score for the sample mean of 34.5 months using the formula: (¯x - μ)/(σ/√n). This gives you (34.5 - 36)/(4/√49) = (-1.5) * 7/4 = -2.62. Notice that since the sample mean lies on the left side of the hypothesised mean of 36 months, the z-score comes out to be negative.</p>
<p><strong>Step 2: Calculate the p-value from the cumulative probability for the given z-score using the z-table. Find out the p-value for a z-score of -2.62 (corresponding to the sample mean of 34.5 months). </strong></p>
<p>Hint: The sample mean is on the left side of the distribution, and it is a two-tailed test.</p>
<ul><li>0.0044</li>
<li>0.9956</li>
<li><strong>0.0088</strong></li>
<li>1.9912</li>
</ul><p>The value in the z-table corresponding to -2.6 on the vertical axis and 0.02 on the horizontal axis is 0.0044. Since the sample mean is on the left side of the distribution and this is a two-tailed test, the p-value would be 2 * 0.0044 = 0.0088.</p>
<p><strong>Step 3: Make the decision on the basis of the p-value with respect to the given value of α (significance value). What would the result of this hypothesis test be?</strong></p>
<ul><li>Fail to reject the null hypothesis</li>
<li><strong>Reject the null hypothesis</strong></li>
</ul><p>Here, the p-value comes out to be 2 * 0.0044 = 0.0088. Since the p-value is less than the significance level (0.0088 < 0.03), you reject the null hypothesis that the average lifespan of the manufacturer's product is 36 months.</p>
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Sun, 17 Jan 2021 10:21:12 +0000tgoswami880 at https://programsbuzz.comHypothesis Testing: Smaller p-values indicate more evidence in support of ___.
https://programsbuzz.com/interview-question/hypothesis-testing-smaller-p-values-indicate-more-evidence-support
<span>Hypothesis Testing: Smaller p-values indicate more evidence in support of ___.</span>
<span><span lang="" about="https://programsbuzz.com/user/1" typeof="schema:Person" property="schema:name" datatype="" xml:lang="">tgoswami</span></span>
<span>Sun, 01/17/2021 - 11:07</span>
<div class="field field--name-body field--type-text-with-summary field--label-hidden field__item"><ul><li>The null hypothesis</li>
<li><strong>The alternative hypothesis</strong></li>
<li>The quality of the researcher</li>
<li>Further testing</li>
</ul><p>The p-value is equivalent to the probability of the null hypothesis not being rejected. So, the smaller the p-value, the farther is the sample mean from the hypothesised population mean, which indicates more evidence in support of the sample mean lying in the critical region, and the alternative hypothesis is accepted.</p>
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Sun, 17 Jan 2021 10:07:24 +0000tgoswami879 at https://programsbuzz.com