Question

cording to a survey, the average young adult male plays video games for 4 hours per week. To test fthe amount of video male plays video games for 4 hours per week. To test if the amount of video est, at a 5% significance level. She surveys 28 male college students randomly and asks them about their amount of video games each week on average. games in college is more than the national average, a researcher decides to do a hypothesist From the data, the sample mean time is 4.4 hours per week, and the sample şta 4 hours per week, and the sample standard deviation (a) is 1.1 hours . a .. 0,05 (significance level) what is the test statistic (t-value) of this one-mean hypothesis test (with σ unknown)? nd your final answer to two decimal places. Provide your answer below: Test Statistic

Answer 1

a) To perform this right-tailed hypothesis test, we use the seven-step method. Step1: The null and altemative hypotheses are as follows Ho: AS4 (The population mean is less than or equal to 4) : μ > 4 (The population mean is greater than 4) Step 2 : We have selected a sample of K-28. We decide to use α-0.05 Step3. Because σ is unknown, we use the 1-distribution and the 1-test statistic We must assume that the population mean are normally distributed Step4: For a given sample size, n, the test statistic t follows at distribution with n-1 degrees of freedom. The critical values of the t distribution with 28-1-27 degrees of freedom The table of t testis obtained by using the Excel2010 function tinv(probabiht, degrees of freedom) =inv(0.05, 27) 1.703288 0a5.2 - 1703288 Step5: The sample mean is X 4.4hours per week. The standard deviation is s 1.1 hours The sample size is n 28 The formula for calculating the t-test statistic is given by X-u 4.4-4 /28 0.4 5.291503 0.4 0.20788 1.924183 192 Step6: The P-value approach r(t >4)=1-P(1-P(t <4)) 1-P(t <1.92) 1 _ 0.96726 0.03274 P-value = ) 3274| <α= 005 we reject the null hypothesis Ho Step7: Conclusion Since, the test statistic is -1.9242 1.703288 We reject the null hypothesis Ho Since, the P-value-0.03274<0.05. We reject the nulll hypothesis H0 There is sufficient evidence to conclude that the population mean time is greater than 4 hours per week.