Question

Consider the following hypothesis test: H0: μ = 15 Ha: μ ≠ 15 A sample of 50 provided a sample mean of 14.12. The population standard deviation is 4. a. Compute the value of the test statistic (to 2 decimals). b. What is the p-value (to 4 decimals)? c. Using α = .05, can it be concluded that the population mean is not equal to 15? Answer the next three questions using the critical value approach. d. Using α = .05, what are the critical values for the test statistic? (+ or -) e. State the rejection rule: Reject H0 if z is the lower critical value and is the upper critical value. f. Can it be concluded that the population mean is not equal to 15?

Answer 1

Solution :

= 15

= 14.12

= 4

n = 50

This is the two tailed test .

The null and alternative hypothesis is ,

H₀ :   = 15

H_a :    15

Test statistic = z

= ( - ) / / n

= (14.12 - 15) /4 / 50

= -1.556

P(z < -1.556 ) = 0.1198

P-value = 0.1198

= 0.05  

= 0.1198 ≥ 0.05, it is concluded that the null hypothesis is not rejected.

There is not enough evidence to claim that the population mean μ is different than 15, at the 0.05 significance level.

The significance level is α=0.05

critical value for a two-tailed test is z_c ​= +1.96 and -1.96

The rejection region for this two-tailed test is R = ( z:∣z∣>1.96 )