Question

In order to conduct a hypothesis test for the population mean, a random sample of 20 observations is drawn from a normally distributed population. The resulting mean and the standard deviation are calculated as 12.9 and 2.4, respectively.

Use the critical value approach to conduct the following tests at α = 0.05.

H0: μ ≤ 12.1 against HA: μ > 12.1

a-1.	Calculate the value of the test statistic. (Round your answer to 2 decimal places.)

Test statistic

a-2.	Calculate the critical value. (Round your answer to 3 decimal places.)

Critical value

a-3.	What is the conclusion?
	Reject H0 since the value of the test statistic is smaller than the critical value. Reject H0 since the value of the test statistic is greater than the critical value. Do not reject H0 since the value of the test statistic is greater than the critical value. Do not reject H0 since the value of the test statistic is smaller than the critical value.

H0: μ = 12.1 against HA: μ ≠ 12.1

b-1.	Calculate the value of the test statistic. (Round your answer to 2 decimal places.)

Test statistic

b-2.	Calculate the critical value(s). (Round your answers to 3 decimal places.)

Critical value(s)

±

b-3.	What is the conclusion?
	Reject H0 since the value of the test statistic is greater than the critical value. Do not reject H0 since the value of the test statistic is smaller than the critical value. Reject H0 since the value of the test statistic is smaller than the critical value. Do not reject H0 since the value of the test statistic is greater than the critical value.

Answer 1

The provided sample mean is and the sample standard deviation is s = 2.4 and the sample size is n = 20

Hypothesis to be tested:

This corresponds to a right-tailed one saample t-test with unknown population standard deviation

The t-statistic is computed as follows:

the significance level is and df=(n-1)=19 hence the critical value for a right-tailed test is

The rejection region for this right-tailed test is
Since it is observed that it is then concluded that the null hypothesis is not rejected.Therefore, there is not enough evidence to claim that the population mean is greater than 12.1, at the 0.05 significance level.

Do not reject H₀ since the vatue of test statistics is smaller than the critical value.

Hypothesis to be tested:

This corresponds to a two-tailed one sample t-test , with unknown population standard deviation

The t-statistic is computed as follows:

the significance level is and df=(n-1)=19 hence the critical value for a two-tailed test is

The rejection region for this right-tailed test is
Since it is observed that it is then concluded that the null hypothesis is not rejected.Therefore, there is not enough evidence to claim that the population mean  is different than 12.1, at the 0.05 significance level.

Do not reject H₀ since the vatue of test statistics is smaller than the critical value.