Question

You wish to test the following claim ( H a ) at a significance level of α = 0.001 .

H o : μ = 77.2

H a : μ < 77.2

You believe the population is normally distributed, but you do not know the standard deviation. You obtain a sample of size n = 16 with mean M = 65.4 and a standard deviation of S D = 15.2 .

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

p-value =

The p-value is...

less than (or equal to) α or greater than α

This p-value leads to a decision to...

reject the null or accept the null or 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 less than 77.2.

b . There is not sufficient evidence to warrant rejection of the claim that the population mean is less than 77.2.

c . The sample data support the claim that the population mean is less than 77.2.

d . There is not sufficient sample evidence to support the claim that the population mean is less than 77.2.

Answer 1

We will conduct a t test for single mean.

To find p value we need to find t value using the formula:

where,

is sample mean

is population mean

s is sample standard deviation

and n is sample size

p value:

**We checked for positive values since the distribution is symmetric. Therefore,