Question

Consider the following hypothesis test:

H ₀:   50

H _a:  > 50

A sample of 60 is used and the population standard deviation is 7. Use the critical value approach to state your conclusion for each of the following sample results. Use  = .05.

a. 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

= 50

n = 60

= 7

The z-critical value for a right-tailed test, for a significance level of α=0.05 is. zc = 1.64

(a) = 52.5

z = 2.77

As z stat falls in the rejection area, we reject the Null hypothesis.

Can it be concluded that the population mean is > 50 : Yes

(b) = 51

z = 1.11

As z stat does not fall in the rejection area, we fail to reject the Null hypothesis.

Can it be concluded that the population mean is > 50 : No

(c)   = 51.8

z = 1.99

As z stat falls in the rejection area, we reject the Null hypothesis.

Can it be concluded that the population mean is > 50 : Yes