Question

From a random sample from normal population, we observed sample mean=84.5 and sample standard deviation=11.2, n = 16, H0: μ = 80, Ha: μ < 80.  State your conclusion about H0 at significance level 0.01.

choices:

A. Test statistic: t = 1.61. P-value = 0.9356. Reject the null hypothesis. There is sufficient evidence to conclude that the mean is less than 80. The evidence against the null hypothesis is very strong.

B. Test statistic: t = 1.61. P-value = 0.0644. Do not reject the null hypothesis. There is not sufficient evidence to conclude that the mean is less than 80. The evidence against the null hypothesis is moderate.

C. Test statistic: t = 1.61. P-value = 0.9463. Do not reject the null hypothesis. There is not sufficient evidence to conclude that the mean is less than 80. The evidence against the null hypothesis is weak or none.

D. Test statistic: t = 1.61. P-value = 0.9356. Do not reject the null hypothesis. There is not sufficient evidence to conclude that the mean is less than 80. The evidence against the null hypothesis is weak or none.

Answer 1

From a random sample from normal population, we observed sample mean=84.5 and sample standard deviation=11.2, n = 16, H0: μ = 80, Ha: μ < 80.  State your conclusion about H0 at significance level 0.01.

choices:

Answer :-  B. Test statistic: t = 1.61. P-value = 0.0644. Do not reject the null hypothesis. There is not sufficient evidence to conclude that the mean is less than 80. The evidence against the null hypothesis is moderate.

The complete sloution of above question are as below

The null and alternative hypothesis is

H0: μ = 80, Ha: μ < 80

Or

The null and alternative hypothesis using the word as

H0 : There is not sufficient evidence to conclude that the mean is less than 80

Ha : There is sufficient evidence to conclude that the mean is less than 80

The values provided in the above question are as below

Sample mean = = 84.5

Sample standard deviation = = 11.2

Sample size = = 16

Population mean = = 80

The formula of test statistic are as below

(Round answer to two decimal places)

Test statistic: t = 1.61

Now, we find P-value of above test statistic using following Excel function

=TDIST(x,deg_freedom, tails)

Here, x = Test statistic: t = 1.607142857 (Here we use test statistic t value without rounding)

deg_freedom = n - 1 = 16 - 1 = 15, tails = 1 (test is left tailed test)

Using above all values in Excel function

=TDIST(1.607142857, 15, 1) then press Enter

=0.064432156 0.0644 (Round answer to four decimal places)

P-value = 0.0644

Now, we comparing the P-value with significance level 0.01 and take decision about the reject or do not reject the null hypothesis.

Here, P-value = 0.0644 > significance level = 0.01

We do not reject the null hypothesis

That is, there is not sufficient evidence to conclude that the mean is less than 80. The evidence against the null hypothesis is moderate.

Answer :-  B. Test statistic: t = 1.61. P-value = 0.0644. Do not reject the null hypothesis. There is not sufficient evidence to conclude that the mean is less than 80. The evidence against the null hypothesis is moderate.

Summary :-

From a random sample from normal population, we observed sample mean=84.5 and sample standard deviation=11.2, n = 16, H0: μ = 80, Ha: μ < 80.  State your conclusion about H0 at significance level 0.01.

choices:

Answer :- B. Test statistic: t = 1.61. P-value = 0.0644. Do not reject the null hypothesis. There is not sufficient evidence to conclude that the mean is less than 80. The evidence against the null hypothesis is moderate.