Question

Soccer. An Asahi News Twitter poll of 1240 teens conducted in 2017 found that girls were more likely than boys to play soccer, by 77% compared to 65% for boys. An equal number of boys and girls were surveyed. Give a 95% confidence interval for the difference in soccer playing by gender.

Which method is this?

a) Define the population parameter in this context.

b) Are these quantitative or categorical data?

c) Do these data satisfy the necessary conditions? Explain each condition. Show me the numbers.

(independence can be skipped)

d) Make an 95% confidence interval and write a sentence interpreting it. You are to write the formula from the cheat sheet, and note each variable in that formula and show work to solve for that variable, including the SE. Then plug in those values to the equation and solve for the CI. Start from left to right as you read the formula so that there is order/consistency to how you do each problem.

e) What would you conclude about the gender of soccer players according to the Asahi News Twitter poll

Now confirm your findings with an appropriate hypothesis test.

1) Find or confirm SE:

2) Find the critical value for alpha:                                                      Sketch

3) Find the test statistic:

4) Find the P-value:

5) Conclusion, and what can you say about the soccer playing by gender?

Answer 1

Solution:

a. Given the following parameters:

= 0.77, = 1240, = 0.65, = 1240

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b. These are categorical data as they are categorised by gender: boys and girls

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c. Since and both are greater than 5, we approximate to normal distribution.

Since and both are greater than 5, we approximate to normal distribution

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d. First, we compute pooled proportion,

= 0.71

95% confidence interval for the difference in the population proportion is given by:-

0.084, 0.156

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e. Since zero does not lie within the interval, we can conclude that girls were more likely than boys to play soccer.