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 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 = 0.96

The 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 = 1.74

The 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.