Question

A researcher was interested in comparing the heights of women in two different countries. Independent simple random samples of 9 women from country A and 9 women from country B yielded the following heights (in inches). 

Country A: 64.1 66.4 61.7 62.0 67.3 64.9 64.7 68.0 

Country B: 65.3 60.2 61.7 65.8 61.0 64.6 60.0 65.4 59.0 

At the 5% significance level, do the data provide sufficient evidence to conclude that the mean height of women in country A is different from the mean height of women in country B? Assume both populations are normal.

 a) State the null and alternative hypotheses symbolically. 

b) Use 1-var-stats to find the sample means and the sample standard deviations. 

c) Check assumptions and choose an appropriate test procedure. 

d) Compute the value of the test statistic. 

e) Determine the P-value. Please show your work. 

f) Decide on the null hypothesis (reject H, or do not reject Ho). 

g) Interpret the results of the hypothesis test.

Answer 1

Here, we are given that a researcher was interested in comparing the heights of women in two different countries. at 5% level of significance we have to test that whether the data provides sufficient evidence to conclude that the mean height of woman in country A is different from the mean height of women in country B.

a) The null and the alternative hypothesis are-

H₀: µ₁ = µ₂ vs H₁: µ₁ ≠ µ₂ where,

: is the true population mean of heights of women in country A.

: is the true population mean of heights of women in country B.

b) To calculate the sample mean and sample sd we consider the following formula-

,

For country A:

= sample mean = 64.74

s = sample sd = 0.19

For country B:

= sample mean = 61.44

s = sample sd = 4.72

c) We have to check for assumptions and choose a appropriate test procedure. We assume that both the populations are normal and have equal variance so we opt for a 2- sample t test.

d) We have to calculate the value of the test statistic which is given by-

Where, n₁ is the sample size of the first sample = 9

               n₂ is the sample size of the first sample = 9

                sample mean of first sample = 64.74

                 sample mean of second sample = 61.44

s is the sample pooled variance = 3.6795

Therefore,

= 1.9