Question

In order to conduct a hypothesis test for the population mean, a random sample of 24 observations is drawn from a normally distributed population. The resulting mean and the standard deviation are calculated as 6.3 and 2.5, respectively. Use Table 2. Use the critical value approach to conduct the following tests at α = 0.05. H0: μ ≤ 5.1 against HA: μ > 5.1 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? Do not reject H0 since the value of the test statistic is less 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. Reject H0 since the value of the test statistic is smaller than the critical value. H0: μ = 5.1 against HA: μ ≠ 5.1 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? 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 greater 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

Answer (5- A)

it is given that sample mean

sample size n =24

population mean

we want to test for the right tailed hypothesis {given in the alternate hypothesis}

test statistics

(a-1)

(a-2) degree of freedom = n- 1 = 24-1 = 23

using excel function T.INV.RT(alpha, df)

setting alpha = 0.05 and df = 23

= T.INV.RT(alpha, df)

= T.INV.RT(0.05,23)

= 1.714

(a-3) Since t statistics is greater than 1.714(t critical value), we can reject the null hypothesis and can conclude that the mean is greater than 5.1

Correct option is Reject H0 since the value of the test statistic is greater than the critical value

Answer 5-B

it is given that sample mean

sample size n =24

population mean

we want to test for the two tailed hypothesis {given in the alternate hypothesis}

test statistics

(a-1)

(a-2) degree of freedom = n- 1 = 24-1 = 23

using excel function T.INV.2T(alpha, df)

setting alpha = 0.05 and df = 23

= T.INV.RT(alpha, df)

= T.INV.RT(0.05,23)

= 2.069

(a-3) Since t statistics is greater than 2.069(t critical value), we can reject the null hypothesis and can conclude that the mean is not equal to 5.1

Correct option is Reject H0 since the value of the test statistic is greater than the critical value