Consider the following hypothesis test:H0: u u is less than or equal to 50Ha: u > 50A sample of 60 is used and the population standard deviation is 8. Use the critical value approach to state your conclusion for each of the following sample results. Use = .05.a. With ?? x = 52.5, what is the value of the test statistic (to 2 decimals)?Can it be concluded that the population mean is greater than 50?b. With ?x? = 51, what is the value of the test statistic (to 2 decimals)?Can it be concluded that the population mean is greater than 50?c. With ?x? = 51.8, what is the value of the test statistic (to 2 decimals)?Can it be concluded that the population mean is greater than 50?

Step-by-step explanation:Because we know the population standard deviation, we must use a Z-test.Null hypothesis (H0): μ=50  Alternative hypothesis (H1): μ> 50 The decision rule is: z-statistic< Z(z-student table (alpha/2)) --> You must accept the null hypothesis z-statistic > Z (z-student table(alpha/2)) --> You must reject the null hypothesis z-statistic formula: z= (xbar-m)/(σ/(sqrt(n))) xbar: sample mean m: hypothesized value σ: population standard deviation n: number of observations a)z=(52.5-50)/(8/sqrt(60)) z= 2.42  The z-distribution table statistic at 2,5% (alpha/2) significance level is: 1.96 Because z-statistic is greater than the z-table value, we must reject the null hypothesis. It can be concluded that the population mean is greater than 50.b)z=(51-50)/(8/sqrt(60)) z= 0.96The z-distribution table statistic at 2,5% (alpha/2)significance level is the same: 1.96 Because z-statistic is less than the z-table value, it cannot be concluded that the population mean is greater than 50.c)z=(51.8-50)/(8/sqrt(60)) z= 1.74The z-distribution table statistic at 2,5%(alpha/2) significance level is the same: 1.96 Because z-statistic is less than the z-table value, it cannot be concluded that the population mean is greater than 50.