Question

You wish to test the following claim ( H a ) at a significance level of α = 0.02 .

H o : μ = 55.7 H a : μ ≠ 55.7

You believe the population is normally distributed, but you do not know the standard deviation. You obtain a sample of size n = 111 with mean M = 50.4 and a standard deviation of S D = 14.8 .

What is the test statistic for this sample? (Report answer accurate to three decimal places.) test statistic

What is the p-value for this sample? (Report answer accurate to four decimal places.)

The p-value is... less than (or equal to) α OR greater than α

This test statistic leads to a decision to: reject the null, accept the null, fail to reject the null

As such, the final conclusion is that:  A) There is sufficient evidence to warrant rejection of the claim that the population mean is not equal to 55.7, B) There is not sufficient evidence to warrant rejection of the claim that the population mean is not equal to 55.7. C) The sample data support the claim that the population mean is not equal to 55.7. D) There is not sufficient sample evidence to support the claim that the population mean is not equal to 55.7.

Answer 1

It is two tailed hypothesis testing

it is given that sample mean = 50.4, sd = 14.8, sample size is n = 111 and population mean = 55.7

t test statistics =

this implies

= - 5.3 /1.405

t statistics = -3.773

degree of freedom = n-1 = 111-1 = 110

using excel function T.DIST.2T(t,df) to get the p value

= T.DIST.2T(-3.773,110)

P value = 0.0003

p value is less than significance level of 0.02 or alpha

Rejecting the null hypothesis as the result is significant

option C is correct