Question

Suppose you have conducted a two tailed hypothesis test for the population mean where the population standard deviation was unknown, the population data is normally distributed, and the sample size is 8. Your test statistic is -1.70. At a level of significance of 0.10, what is your conclusion?

A. Reject the null hypothesis since the test statistic is between the critical values.

B. Do not reject the null hypothesis since the test statistic is between the critical values.

C. Reject the null hypothesis since the test statistic is greater than the critical values.

D. Reject the null hypothesis since the test statistic is less than the critical values.

Suppose you have the following null and alternative hypotheses: H₀: μ = 38 and H₁: μ ≠ 38.

You collect a sample of data from a population that is normally distributed . The sample size is 16, the sample mean is 36.2, and the sample standard deviation is 7.

What is your p-value and conclusion? Test at a level of significance of 0.05.

A. 0.1518, Do Not Reject

B. 0.3200, Do Not Reject

C. 0.3048, Do Not Reject

D. 0.3037, Do Not Reject

E. 0.3200, Reject

F. 0.3037, Reject

Answer 1

Q.1) Given that, sample size ( n ) = 8

Test statistic for two-tailed t-test is, t = -1.70

t-critical values at level of significance of 0.10 with degrees of freedom = 8 - 1= 7 are, t^* = ± 1.895

Here, test statistic = -1.70 is between -1.895 and +1.895

Therefore, we Do not reject the null hypothesis since the test statistic is between the critical values.

Answer: B)

Q.2) Given that, sample size ( n )= 16

sample mean = 36.2 and sample standard deviation = 7

The null and alternative hypotheses are,

H0: μ = 38 and H1: μ ≠ 38

Using TI-84 calculator we get,

Test statistic = -1.0286

p-value = 0.3200

Since, p-value = 0.3200 > 0.05, we do not reject the null hypothesis.

Answer : B) 0.3200, Do Not Reject