Question

Bob claims that a population mean u=94. The value of the population standard deviation is known to be o=10. To test Bob's claim, we take a simple random sample of size n=70 from this population. The sample mean turns out to be x=107. Use the information from the sample to test Bob's claim at the a(alpha) =0.05 significance level. Report the final result of the hypothesis test.

A. Reject the null hypothesis B. Cannot reject the null hypothesis

Answer 1

Solution :

This is the two tailed test .

The null and alternative hypothesis is ,

H₀ :   = 94

H_a :    94

Test statistic = z

= ( - ) / / n

= (107 - 94) / 10 / 70

= 10.88

P(z > 10.88) = 1 - P(z < 10.88) = 0

P-value = 2 * 0 = 0

= 0.05

P-value <

Reject the null hypothesis .