1. Future parents undergoing some types of fertility treatments can choose the s
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Question
1. Future parents undergoing some types of fertility treatments can choose the sex of their child. A study in the journal Fertility and Sterility reported that among 229 women who wanted to choose their baby’s sex, 89 wanted a boy and 140 wanted a girl. a) Let p = the true proportion of women who want to choose their baby’s sex and choose a boy. Write a set of hypotheses in symbols to test the claim that boys and girls are not equally preferred. b) Using = 0.05, should the null hypothesis be rejected or not rejected? c) Multiple choice: Select the proper interpretation for these test results. i. I did not find enough evidence to show that boys and girls are unequally preferred. ii. I did not find enough evidence to show that boys and girls are equally preferred. iii. I found enough evidence to show that boys and girls are unequally preferred. iv. I found enough evidence to show that boys and girls are equally preferred. d) Based on your P-value and = 0.05, which type of error might have occurred: type I or type II? 2. A survey asked 1000 randomly selected adult Americans if they have health insurance or not. The results of the survey were used to make the following bootstrap distribution, showing the proportion per bootstrap sample who did have insurance: a) How many of the people surveyed did have health insurance? b) Calculate a 95% confidence interval using the “2 standard errors” method. c) In one sentence, interpret your interval from part b, being as specific as possible about what the interval describes. d) For a 90% CI, what percentage of statistics would need to be excluded from each tail? e) For a 90% CI, exactly how many statistics would need to be excluded from each tail of this bootstrap distribution? f) For each of the following pairs, indicate whether the relationship is positive (one increases other increases) or negative (one increases other decreases): i. sample size (n) and standard error ii. sample size (n) and interval width iii. confidence level and interval width iv. confidence level and margin of error 3. For the CI interpretations below, identify whether each is valid or invalid. If invalid, edit the statement into a valid interpretation. a) I am 95% sure that the mean rent of 20 Manhattan apartments is between $2682 and $3830. b) I am 95% sure that the pH of lakes in Florida is between 6.2 and 6.9. c) I am 95% sure that the confidence interval for mean commute distance of Atlanta commuters is between 17.0 and 19.5 miles. d) I am 95% sure that the mean advertised price for classic Mustang cars is between $12,040 and $20,916.
Explanation / Answer
1. Future parents undergoing some types of fertility treatments can choose the sex of their child. A study in the journal Fertility and Sterility reported that among 229 women who wanted to choose their baby’s sex, 89 wanted a boy and 140 wanted a girl.
a) Let p = the true proportion of women who want to choose their baby’s sex and choose a boy. Write a set of hypotheses in symbols to test the claim that boys and girls are not equally preferred.
Ho: p = 0.5
Ha: p =/= 0.5 [ANSWER]
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b) Using = 0.05, should the null hypothesis be rejected or not rejected?
Formulating the null and alternatuve hypotheses,
Ho: p = 0.5
Ha: p =/= 0.5
As we see, the hypothesized po = 0.5
Getting the point estimate of p, p^,
Here,
x = 89
n = 89+140 = 229
p^ = x / n = 89/(89+140) = 0.388646288
Getting the standard error of p^, sp,
sp = sqrt[po (1 - po)/n] = 0.03304093
Getting the z statistic,
z = (p^ - po)/sp = -3.370174862
As this is a 2 tailed test, then, getting the p value,
p = 0.000751205
As P < 0.05, we REJECT THE NULL HYPOTHESIS. [ANSWER]
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c) Multiple choice: Select the proper interpretation for these test results.
iii. I found enough evidence to show that boys and girls are unequally preferred. [ANSWER]
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d) Based on your P-value and = 0.05, which type of error might have occurred: type I or type II?
As we rejected Ho, we might have had a TYPE I ERROR. [ANSWER]
[Note: A type I error is incorrectly rejecting Ho.]
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