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After a lot of hard work, a studio releases a new video game. The studio believes that the game will be liked by players. In particular, the studio claims that the mean player rating, μ, will be higher than 78. In a random sample of 36 players, the mean rating is 80.4. Assume the population standard deviation of the ratings is known to be 13.8. Is there enough evidence to support the claim that the mean player rating is higher than 78? Perform a hypothesis test, using the 0.05 level of significance. (a) State the null hypothesis Ho and the alternative hypothesis H₁. Ho: H₁:0 • 20.05 is the value that cuts off an area of 0.05 in the right tail. Standard Normal Distribution Step 1: Select one-tailed or two-tailed. O One-tailed O Two-tailed н Step 2: Enter the critical value(s). (Round to 3 decimal places.) ロ<ロ • The test statistic has a normal distribution and the value is given by z= Step 3: Enter the test statistic. (Round to 3 decimal places.) ロマロ X (b) Perform a hypothesis test. The test statistic has a normal distribution (so the test is a "Z-test"). Here is some other information to help you with your test. X OSO 0=0 0*0 O 04- 0.3+ O>O 0.2+ 0.1+ S X S (c) Based on your answer to part (b), choose what can be concluded, at the 0.05 level of significance, about the claim made by the studio. O Since the value of the test statistic lies in the rejection region, the null hypothesis is rejected. So, there is enough evidence to support the claim that the mean player rating is higher than 78. O Since the value of the test statistic lies in the rejection region, the null hypothesis is not rejected. So, there is not enough evidence to support the claim that the mean player rating is higher than 78. O Since the value of the test statistic doesn't lie in the rejection region, the null hypothesis is rejected. So, there is enough evidence to support the claim that the mean player rating is higher than 78. O Since the value of the test statistic doesn't lie in the rejection region, the null hypothesis is not rejected. So, there is not enough evidence to support the claim that the mean player rating is higher than 78. X

After a lot of hard work, a studio releases a new video game. The studio believes that the game will be liked by players. In particular, the studio claims that the mean player rating, μ, will be higher than 78. In a random sample of 36 players, the mean rating is 80.4. Assume the population standard deviation of the ratings is known to be 13.8. Is there enough evidence to support the claim that the mean player rating is higher than 78? Perform a hypothesis test, using the 0.05 level of significance. (a) State the null hypothesis Ho and the alternative hypothesis H₁. Ho: H₁:0 • 20.05 is the value that cuts off an area of 0.05 in the right tail. Standard Normal Distribution Step 1: Select one-tailed or two-tailed. O One-tailed O Two-tailed н Step 2: Enter the critical value(s). (Round to 3 decimal places.) ロ<ロ • The test statistic has a normal distribution and the value is given by z= Step 3: Enter the test statistic. (Round to 3 decimal places.) ロマロ X (b) Perform a hypothesis test. The test statistic has a normal distribution (so the test is a "Z-test"). Here is some other information to help you with your test. X OSO 0=0 0*0 O 04- 0.3+ O>O 0.2+ 0.1+ S X S (c) Based on your answer to part (b), choose what can be concluded, at the 0.05 level of significance, about the claim made by the studio. O Since the value of the test statistic lies in the rejection region, the null hypothesis is rejected. So, there is enough evidence to support the claim that the mean player rating is higher than 78. O Since the value of the test statistic lies in the rejection region, the null hypothesis is not rejected. So, there is not enough evidence to support the claim that the mean player rating is higher than 78. O Since the value of the test statistic doesn't lie in the rejection region, the null hypothesis is rejected. So, there is enough evidence to support the claim that the mean player rating is higher than 78. O Since the value of the test statistic doesn't lie in the rejection region, the null hypothesis is not rejected. So, there is not enough evidence to support the claim that the mean player rating is higher than 78. X

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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After a lot of hard work, a studio releases a new video game. The studio believes that the game will be liked by players. In particular, the studio claims that the mean player rating, μ, will be higher than 78. In a random sample of 36 players, the mean rating is 80.4. Assume the population standard deviation of the ratings is known to be 13.8. Is there enough evidence to support the claim that the mean player rating is higher than 78? Perform a hypothesis test, using the 0.05 level of significance. (a) State the null hypothesis Ho and the alternative hypothesis H₁ . Ho: H₁:0 Standard Normal Distribution Step 1: Select one-tailed or two-tailed. O One-tailed O Two-tailed μ Step 2: Enter the critical value(s). (Round to 3 decimal places.) Step 3: Enter the test statistic. (Round to 3 decimal places.) O<O OSO 020 X X x-μ • The test statistic has a normal distribution and the value is given by z= In (b) Perform a hypothesis test. The test statistic has a normal distribution (so the test is a "Z-test"). Here is some other information to help you with your test. • 20.05 is the value that cuts off an area of 0.05 in the right tail. 0=0 0.3+ 0.2+ ☐> ☐#0 0.1+ 3 (c) Based on your answer to part (b), choose what can be concluded, at the 0.05 level of significance, about the claim made by the studio. O Since the value of the test statistic lies in the rejection region, the null hypothesis is rejected. So, there is enough evidence to support the claim that the mean player rating is higher than 78. O Since the value of the test statistic lies in the rejection region, the null hypothesis is not rejected. So, there is not enough evidence to support the claim that the mean player rating is higher than 78. O Since the value of the test statistic doesn't lie in the rejection region, the null hypothesis is rejected. So, there is enough evidence to support the claim that the mean player rating is higher than 78. O Since the value of the test statistic doesn't lie in the rejection region, the null hypothesis is not rejected. So, there is not enough evidence to support the claim that the mean player rating is higher than 78.
Transcribed Image Text:After a lot of hard work, a studio releases a new video game. The studio believes that the game will be liked by players. In particular, the studio claims that the mean player rating, μ, will be higher than 78. In a random sample of 36 players, the mean rating is 80.4. Assume the population standard deviation of the ratings is known to be 13.8. Is there enough evidence to support the claim that the mean player rating is higher than 78? Perform a hypothesis test, using the 0.05 level of significance. (a) State the null hypothesis Ho and the alternative hypothesis H₁ . Ho: H₁:0 Standard Normal Distribution Step 1: Select one-tailed or two-tailed. O One-tailed O Two-tailed μ Step 2: Enter the critical value(s). (Round to 3 decimal places.) Step 3: Enter the test statistic. (Round to 3 decimal places.) O<O OSO 020 X X x-μ • The test statistic has a normal distribution and the value is given by z= In (b) Perform a hypothesis test. The test statistic has a normal distribution (so the test is a "Z-test"). Here is some other information to help you with your test. • 20.05 is the value that cuts off an area of 0.05 in the right tail. 0=0 0.3+ 0.2+ ☐> ☐#0 0.1+ 3 (c) Based on your answer to part (b), choose what can be concluded, at the 0.05 level of significance, about the claim made by the studio. O Since the value of the test statistic lies in the rejection region, the null hypothesis is rejected. So, there is enough evidence to support the claim that the mean player rating is higher than 78. O Since the value of the test statistic lies in the rejection region, the null hypothesis is not rejected. So, there is not enough evidence to support the claim that the mean player rating is higher than 78. O Since the value of the test statistic doesn't lie in the rejection region, the null hypothesis is rejected. So, there is enough evidence to support the claim that the mean player rating is higher than 78. O Since the value of the test statistic doesn't lie in the rejection region, the null hypothesis is not rejected. So, there is not enough evidence to support the claim that the mean player rating is higher than 78.
The mean SAT score in mathematics is 531. The standard deviation of these scores is 42. A special preparation course claims that the mean SAT score, u, of its graduates is greater than 531. An independent researcher tests this by taking a random sample of 14 students who completed the course; the mean SAT score in mathematics for the sample was 540. Assume that the population is normally distributed. At the 0.10 level of significance, can we conclude that the population mean SAT score for graduates of the course is greater than 531? Assume that the population standard deviation of the scores of course graduates is also 42. Perform a one-tailed test. Then complete the parts below. Carry your intermediate computations to three or more decimal places, and round your responses as specified below. (If necessary, consult a list of formulas.) (a) State the null hypothesis H. and the alternative hypothesis H₁ . Ho: μ ≤ 531 H₁ : µ > 531 (b) Determine the type of test statistic to use. Z (c) Find the value of the test statistic. (Round to three or more decimal places.) 0 (d) Find the p-value. (Round to three or more decimal places.) 0 (e) Can we support the preparation course's claim that the population mean SAT score of its graduates is greater than 531? Yes O No μ XI □≠ロ a 0=0 OSO X S O<O р Ś <Q ☐<0
Transcribed Image Text:The mean SAT score in mathematics is 531. The standard deviation of these scores is 42. A special preparation course claims that the mean SAT score, u, of its graduates is greater than 531. An independent researcher tests this by taking a random sample of 14 students who completed the course; the mean SAT score in mathematics for the sample was 540. Assume that the population is normally distributed. At the 0.10 level of significance, can we conclude that the population mean SAT score for graduates of the course is greater than 531? Assume that the population standard deviation of the scores of course graduates is also 42. Perform a one-tailed test. Then complete the parts below. Carry your intermediate computations to three or more decimal places, and round your responses as specified below. (If necessary, consult a list of formulas.) (a) State the null hypothesis H. and the alternative hypothesis H₁ . Ho: μ ≤ 531 H₁ : µ > 531 (b) Determine the type of test statistic to use. Z (c) Find the value of the test statistic. (Round to three or more decimal places.) 0 (d) Find the p-value. (Round to three or more decimal places.) 0 (e) Can we support the preparation course's claim that the population mean SAT score of its graduates is greater than 531? Yes O No μ XI □≠ロ a 0=0 OSO X S O<O р Ś <Q ☐<0
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