You wish to test the following claim (HaHa ) at a significance level of =0.005=0

Question

You wish to test the following claim (HaHa ) at a significance level of =0.005=0.005 .      

Ho:=86.5Ho:=86.5
Ha:>86.5Ha:>86.5

You believe the population is normally distributed, but you do not know the standard deviation. You obtain a sample of size n=14n=14 with mean ¯x=98.2x¯=98.2 and a standard deviation of s=11.2s=11.2 .

What is the test statistic for this sample?

test statistic = Round to 3 decimal places

What is the p-value for this sample?

p-value = Use Technology Round to 4 decimal places.

The p-value is...

less than (or equal to)

greater than

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...

There is sufficient evidence to warrant rejection of the claim that the population mean is greater than 86.5.

There is not sufficient evidence to warrant rejection of the claim that the population mean is greater than 86.5.

The sample data support the claim that the population mean is greater than 86.5.

There is not sufficient sample evidence to support the claim that the population mean is greater than 86.5.

Explanation / Answer

Here sample size is less than 30 so we will use t statistics

t=xbar-mean(/sd/sqrt(n))

=> t=98.2-86.5/(11.2/sqrt(14))=11.7/2.99=3.913

Here alpha is 0.005 and df is 13 p value is 0.00089768 (using calculator for right tail)

A low P value suggests that your sample provides enough evidence that you can reject the null hypothesis for the entire population.

p< aplha so we reject the null hypothesis

The sample data support the claim that the population mean is greater than 86.5

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