Question

In Country​ A, the population mean height for​ 3-year-old boys is 37 inches. Suppose a random sample of 15​ 3-year-old boys from Country B showed a sample mean of 36.5 inches with a standard deviation of 4 inches. The boys were independently sampled. Assume that heights are Normally distributed in the population. Complete parts a through c below. a. Determine whether the population mean for Country B boys is significantly different from the Country A mean. Use a significance level of 0.05. Find test statistic and p-value b. Now suppose the sample consists of 30 boys instead of 15 and repeat the test. Find the test statistic and p- value

Answer 1

Given,

Hypothesized Mean (μ₀​) = 37 inches

Sample mean ( ) = 36.5 inches

Sample standard deviation (s) = 4 inches

Sample size (n) = 15

Significance level (α) =0.05

Degree of freedom (df) = n -1 = 15 -1 = 14

Null and Alternative Hypotheses

The following null and alternative hypotheses need to be tested:

H_o: μ = 37

H_a: μ ≠ 37

This corresponds to a two-tailed test, for which a t-test for one mean will be used.

Test Statistics

The t-statistic is computed as follows:

The p-value corresponding to df = 14 and t = -0.484 , using t-table(or calculator) we get

p-value = 0.6358

Now taking sample size (n) = 30

df = 30 -1 = 29

The t-statistic is computed as follows:

The p-value corresponding to df = 29  and t = -0.685 , using t-table(or calculator) we get

p-value = 0.499