Question

An anthropologist wanted to know why certain countries were so popularly represented among the elite chess players of the world. Hypothesizing that it may be linked to the amount of youth involvement in the countries, he and colleagues took random samples of children aged 12 or less in a variety of countries across the world and asked them if they played chess. The results from two countries are shown below.

Country	n	Number who play chess
USA	294	171
Russia	269	180

a) What is the correct hypothesis to test if there is a difference in youth involvement in chess between the two countries?

H₀: p₁-p₂=0 vs. H_a: p₁-p₂≠0H₀: μ₁-μ₂=0 vs. H_a: μ₁-μ₂≠0    H₀: p̂₁-p̂₂=0 vs. H_a: p̂₁-p̂₂≠0H₀: x₁ - x₂ = 0 vs. H_a: x₁ - x₂ ≠ 0

b) Suppose that instead of being provided the data, you were only told that the p-value for the test is 0.032. Using this p-value, what would we conclude at α = .05?

Reject the null hypothesis; there is evidence of different levels of youth involvement in chess between the two countries.Do not reject the null hypothesis; there is not enough evidence to conclude that the two countries have the same level of youth participation.    The difference in youth participation is responsible for the difference in representation for the two countries among the game's elite.Reject the null hypothesis; there is not enough evidence of different levels of youth involvement in chess between the two countries.

c) Using that same p-value from part b), which of the following statements are true? Select all that apply.

0 would be inside a 95% confidence interval.

0 would not be inside a 95% confidence interval.

We do not know if 0 will be inside the 95% confidence interval.0 would be inside a 99% confidence interval.

0 would not be inside a 99% confidence interval.We do not know if 0 will be inside the 99% confidence interval.

Answer 1

Solution:

Part a) What is the correct hypothesis to test if there is a difference in youth involvement in chess between the two countries?

Since we have  to test if there is a difference in youth involvement in chess between the two countries, that is we have to test if there is difference in proportions of youth involvement in chess between the two countries, thus we use two population proportion test.

Thus hypothesis are:

H₀: p₁-p₂=0 vs. H_a: p₁-p₂≠0

Part b) Suppose that instead of being provided the data, you were only told that the p-value for the test is 0.032. Using this p-value, what would we conclude at α = .05?

Decision Rule: Reject null hypothesis H0, if p-value < 0.05 level of significance , otherwise we fail to reject H0.

Since p-value = 0.032 < 0.05 level of significance , we reject null hypothesis H0. That means there is difference in youth involvement in chess between the two countries.

Thus correct option is:
Reject the null hypothesis; there is evidence of different levels of youth involvement in chess between the two countries.

Part c) Using that same p-value from part b), which of the following statements are true?

for 95% confidence level , level of significance = 1 -0.95=0.05

If p-value is 0.032 < 0.05 level of significance , then we reject H0 and difference is difference from 0

thus 0 would not be inside a 95% confidence interval.

For 99% confidence interval , level of significance = 1 -c = 1 -0.99 = 0.01

Since p-value = 0.032 > 0.01, so in this case we fail to reject null hypothesis means there is no difference

that means difference is null that is 0,

thus 0 would be inside a 99% confidence interval.

Thus we have two correct answers:

0 would NOT be inside a 95% confidence interval.

0 would be inside a 99% confidence interval.