1. A simple random sample of 200 married people were asked the question, “Would
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Question
1. A simple random sample of 200 married people were asked the question, “Would you remarry your spouse a second time if you were given the chance?”. Based on the 200 responses, a 95% confidence interval for the proportion of people who reported they would remarry their spouse is (.812,.908). Which of the following is the correct interpretation of the confidence interval?
We are 95% confident that between 81.2% and 90.8% of the next 200 married people surveyed would be willing to remarry their spouse.
We are 95% confident that the true proportion of people who would remarry their spouse is between 81.2% and 90.8%.
c) The probability that 95% of people would remarry their spouse is between .812 and .908.
95% of all confidence intervals calculated regarding the proportion of people who would remarry their spouse a second time will contain the sample proportion of .86.
2. If the sample proportion had been .90 instead of .86 as observed in the original poll while still using a sample size of 200 and a 95% confidence interval, then the confidence interval would have been:
a) Wider
b) Narrower
c) The same width
3. Which of the following statements are true based on the confidence interval? Could be more than one.
a) The proportion of people who would remarry their spouse appears to be significantly greater than .80.
.90 is a plausible estimate for the true proportion of people who would remarry their spouse.
A 90% confidence interval would contain .80
4. Suppose a simple random sample of 800 recently divorced men are surveyed in a separate poll and asked the same question regarding if they would remarry their spouse. A 95% confidence interval is calculated for these responses as well. Which of the following statements is not true?
a) The sample proportion of divorced men who reported they would remarry their spouse should not be used to approximate the proportion of all people who would remarry their spouse because the estimate is likely biased downward.
b) The intervals are estimating different parameters so no conclusions can be made about the proportion of all married people who would remarry their spouse based on the interval that consisted of only divorced men.
c) The interval calculated from the sample of divorced men is a closer approximation of the proportion of people who would remarry their spouse because the sample size is larger
d) The interval calculated from the sample of divorced men will be narrower than the interval calculated by taking the sample from the population of people who are currently married.
5. What is the chi-squared contribution from the category ‘Extra Large’?
a) 0.125
b) -0.125
c) -0.143
d) 0.147
e) 1.875
f) 2.143
6. How many degrees of freedom does this test have?
a) 4
b) 600
c) 3
d) 599
7. What conclusion can we come to based on the results of the test and the confidence intervals?
a) The proportion of large shirts sold differs significantly from its hypothesized proportion.
b)None of the proportions of shirt sizes sold differ significantly from their hypothesized proportions.
c) The proportion of all four shirt sizes differ significantly from their hypothesized proportions.
d) Only the proportion of large shirts sold differs significantly from its hypothesized proportion.
e) Only the proportion of extra-large shirts sold differs significantly from its hypothesized proportion.
f) The proportion of small, medium, and extra-large shirts differ significantly from their hypothesized proportions.
a)We are 95% confident that between 81.2% and 90.8% of the next 200 married people surveyed would be willing to remarry their spouse.
b)We are 95% confident that the true proportion of people who would remarry their spouse is between 81.2% and 90.8%.
c) The probability that 95% of people would remarry their spouse is between .812 and .908.
d)95% of all confidence intervals calculated regarding the proportion of people who would remarry their spouse a second time will contain the sample proportion of .86.
Explanation / Answer
1. A confidence interval does not quantify variability. A 95% confidence interval is a range of values that you can be 95% certain contains the true mean of the population. This is not the same as a range that contains 95% of the values.
Hence answer is b. We are 95% confident that the true proportion of people who would remarry their spouse is between 81.2% and 90.8%.
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