B Explain what this interval means

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Hypothesis testing problem set

According to official census figures, 8% of couples living together are not married. A researcher took a random sample of 400 couples and found that 9.5% of them are not married. Test at the 15% significance level if the current percentage of unmarried couples is different from 8%.
Any basketball fan knows that Shaquille O’Neal, one of the NBA’s most dominant centers of the last twenty years, always had difficulty shooting free throws. Over the course of his career, his overall made free-throw percentage was 53.3%. During one offseason, Shaq had been working with an assistant coach on his free-throw technique. During the next season, a simple random sample showed that Shaq made 26 of 39 free-throw attempts. Test the claim at the 0.05 SL that Shaq has significantly improved his free-throw shooting.
According to a study, 21.1% of 507 female college students were on a diet at the time of the study.
a) Construct a 99% confidence interval for the true proportion of all female students who were on a diet at the time of this study.
b) Explain what this interval means.
c) Is it reasonable to think that only 17% of college women are on a diet?
Two Polish math professors and their students spun a Belgian euro coin 250 times. It landed on heads 140 times. One of the professors concluded that the coin was minted asymmetrically. A representative from the Belgian mint said that the result was just by chance. Is the math professor or the representative from the Belgian mint correct? At the 0.01 SL test the math professor’s claim that the coin is not fair.
A sample of 800 items produced on a new machine showed that 48 of them are defective. The factory will get rid the machine if the data indicates that the proportion of defective items is significantly more than 5%. At a significance level of 10% does the factory get rid of the machine or not?
Example A study of teenage suicide included a sample of 96 boys and 123 girls between ages of 12 and 16 years selected scientifically from admissions records to a private psychiatric hospital. Suicide attempts were reported by 18 of the boys and 60 of the girls. We assume that the girls constitute a simple random sample from a population of similar girls and likewise for the boys. Construct a 99 percent confidence interval for the difference between the two proportions.
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