Question

Consider the following hypothesis test:

H ₀:   50

H _a:  > 50

A sample of 55 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.

With  = 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?
SelectYesNoItem 2

b. With  = 51, what is the value of the test statistic (to 2 decimals)?
  

Can it be concluded that the population mean is greater than 50?
SelectYesNoItem 4

c. With  = 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?
SelectYesNoItem 6

Answer 1

H0: mean <= 50

H1: mean > 50

sample size (n) = 55; standard deviation (sd) = 8; alpha = 0.05;

a). x = 52.5

z-value = (x - mean)/sd/n^0.5

= (52.5 - 50)/(8/55^0.5) = 2.32 (Test statistic)

P-value = Probability (z > 2.32) = 1 - Probability (z < 2.32) = 1 - 0.9898 = 0.0102

This p-value is less than alpha so so H0 is rejected. Yes, it can be concluded that the population mean is greater than 50.

b). x = 51

z-value = (51-50)/(8/55^0.5) = 0.93 (Test statistic)

p-value = Probability(z > 0.93) = 1 - Probability(z < 0.93) = 1 - 0.8238 = 0.1762

p-value is greater than alpha so H0 is accepted. No, it cannot be concluded that the population mean is greater than 50.

c). x = 51.8

z-value = (51.8-50)/(8/55^0.5) = 1.67 (Test statistic)

p-value = Probability(z > 1.67) = 1 - Probability(z < 1.67) = 1 - 0.9525 = 0.0475

p-value is less than alpha so H0 is rejected. Yes, it can be concluded that the population mean is greater than 50.