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(a) State the null hypothesis Ho and the alternative hypothesis H₁ that you would use for the test. Ho: p = 0.32 H₁: p > 0.32 Р ê O 10 and n (1-p) ≥ 10 under the assumption that the null hypothesis is true.) Heren is the sample size and p is the population proportion you are testing.

(a) State the null hypothesis Ho and the alternative hypothesis H₁ that you would use for the test. Ho: p = 0.32 H₁: p > 0.32 Р ê O 10 and n (1-p) ≥ 10 under the assumption that the null hypothesis is true.) Heren is the sample size and p is the population proportion you are testing.

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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According to past studies, 32% of gamers experience motion sickness from using virtual reality (VR) glasses. Because of changes to the way VR glasses are manufactured, a consumer advocate claims the proportion, p, of gamers who will experience motion sickness from using modern VR glasses is more than 32%. He tests his claim by choosing 185 gamers at random and having each of them use a pair of newly-manufactured VR glasses. Of these gamers, 72 say that using the glasses makes them motion sick. Complete the parts below to perform a hypothesis test to see if there is enough evidence, at the 0.05 level of significance, to conclude that the proportion, p, of all gamers who will experience motion sickness from using modern VR glasses is greater than 32%. (a) State the null hypothesis Ho and the alternative hypothesis H₁ that you would use for the test. Ho: p = 0.32 H₁: p > 0.32 Р np = 59.2 n (1-p) = 125.8 ロ<ロ OSO Â X 020 ロ=ロ 0#0 O<O (b) For your hypothesis test, you will use a Z-test. Find the values of np and n (1-p) to confirm that a Z-test can be used. (One standard is that np ≥ 10 and n (1-p) ≥ 10 under the assumption that the null hypothesis is true.) Here is the sample size and p is the population proportion you are testing. • The value of the test statistic is given by z = (c) Perform a Z-test. Here is some information to help you with your Z-test. • 20.05 is the value that cuts off an area of 0.05 in the right tail of the distribution. P-P p(1-p) n
Transcribed Image Text:According to past studies, 32% of gamers experience motion sickness from using virtual reality (VR) glasses. Because of changes to the way VR glasses are manufactured, a consumer advocate claims the proportion, p, of gamers who will experience motion sickness from using modern VR glasses is more than 32%. He tests his claim by choosing 185 gamers at random and having each of them use a pair of newly-manufactured VR glasses. Of these gamers, 72 say that using the glasses makes them motion sick. Complete the parts below to perform a hypothesis test to see if there is enough evidence, at the 0.05 level of significance, to conclude that the proportion, p, of all gamers who will experience motion sickness from using modern VR glasses is greater than 32%. (a) State the null hypothesis Ho and the alternative hypothesis H₁ that you would use for the test. Ho: p = 0.32 H₁: p > 0.32 Р np = 59.2 n (1-p) = 125.8 ロ<ロ OSO Â X 020 ロ=ロ 0#0 O<O (b) For your hypothesis test, you will use a Z-test. Find the values of np and n (1-p) to confirm that a Z-test can be used. (One standard is that np ≥ 10 and n (1-p) ≥ 10 under the assumption that the null hypothesis is true.) Here is the sample size and p is the population proportion you are testing. • The value of the test statistic is given by z = (c) Perform a Z-test. Here is some information to help you with your Z-test. • 20.05 is the value that cuts off an area of 0.05 in the right tail of the distribution. P-P p(1-p) n
Standard Normal Distribution Step 1: Select one-tailed or two-tailed. O One-tailed O Two-tailed Step 2: Enter the critical value(s). (Round to 3 decimal places.) Step 3: Enter the test statistic. (Round to 3 decimal places.) 04 0.3+ 02+ 0.1+ X (d) Based on your answer to part (c), choose what can be concluded, at the 0.05 level of significance, about the proportion of all gamers who will experience motion sickness from using modern VR glasses. O Since the value of the test statistic lies in the rejection region, the null hypothesis is rejected. So, there is enough evidence to conclude that more than 32% of all gamers will experience motion sickness from using modern VR glasses. 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 conclude that more than 32% of all gamers will experience motion sickness from using modern VR glasses. 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 conclude that more than 32% all gamers will experience motion sickness from using modern VR glasses. 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 conclude that more than 32% of all gamers will experience motion sickness from using modern VR glasses. X
Transcribed Image Text:Standard Normal Distribution Step 1: Select one-tailed or two-tailed. O One-tailed O Two-tailed Step 2: Enter the critical value(s). (Round to 3 decimal places.) Step 3: Enter the test statistic. (Round to 3 decimal places.) 04 0.3+ 02+ 0.1+ X (d) Based on your answer to part (c), choose what can be concluded, at the 0.05 level of significance, about the proportion of all gamers who will experience motion sickness from using modern VR glasses. O Since the value of the test statistic lies in the rejection region, the null hypothesis is rejected. So, there is enough evidence to conclude that more than 32% of all gamers will experience motion sickness from using modern VR glasses. 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 conclude that more than 32% of all gamers will experience motion sickness from using modern VR glasses. 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 conclude that more than 32% all gamers will experience motion sickness from using modern VR glasses. 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 conclude that more than 32% of all gamers will experience motion sickness from using modern VR glasses. X
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