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 36.8 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. Part B: Find the test statistic. Find the​ p-value. Reject or do not reject Upper Ho.

Answer 1

a)

Below are the null and alternative Hypothesis,
Null Hypothesis: μ = 37
Alternative Hypothesis: μ ≠ 37

Rejection Region
This is two tailed test, for α = 0.05 and df = 14
Critical value of t are -2.145 and 2.145.
Hence reject H0 if t < -2.145 or t > 2.145

Test statistic,
t = (xbar - mu)/(s/sqrt(n))
t = (36.8 - 37)/(4/sqrt(15))
t = -0.194

As the value of test statistic, t is outside critical value range, fail to reject the null hypothesis

b)

Test statistic,
t = (xbar - mu)/(s/sqrt(n))
t = (36.8 - 37)/(4/sqrt(15))
t = -0.194

c)

P-value Approach
P-value = 0.849
As P-value >= 0.05, fail to reject null hypothesis.