Question

You wish to test the following claim ( H 1 ) at a significance level of α = 0.01 . H 0 : μ = 70.2 H 1 : μ < 70.2 You believe the population is normally distributed, but you do not know the standard deviation. You obtain a sample of size n = 19 with mean ¯ x = 59.9 and a standard deviation of s = 11.8 .

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.) p-value =

The p-value is... less than (or equal to) α 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... There is sufficient evidence to warrant rejection of the claim that the population mean is less than 70.2. There is not sufficient evidence to warrant rejection of the claim that the population mean is less than 70.2. The sample data support the claim that the population mean is less than 70.2. There is not sufficient sample evidence to support the claim that the population mean is less than 70.2.

Answer 1

Let's write the given information

n = sample size = 19

= sample mean = 59.9

s = sample standard deviation = 11.8

From the alternative hypothesis the given test is left tailed test

Here population standard deviation is not given and we use sample standard deviation(s) instead of population

standard deviation . So we can used one sample t test

Using minitab we get following result

The command is Stat>>>Basic Statistics >>1 sample t...

Select summary Statistics

then click on Perform hypothesis test enter hypothesis mean (70.2)

then click on Option select level of confidence = (1 - alpha)*100 = (1 - 0.01)*100 = 99.0

Alternative " less than"

Look the following image:

then click on Ok

We get the following output

From the above output

t test statistic value = -3.80

p- value = 0.001

Decision rule: 1) If p-value < level of significance (alpha) then we reject null hypothesis

2) If p-value > level of significance (alpha) then we fail to reject null hypothesis.

Here p value = 0.001 < 0.01 so we used first rule.

That is we reject null hypothesis and accept alternative hypothesis.

So correct option is: "The sample data support the claim that the population mean is less than 70.2" .