Answer the following questions:

1. Two 95% confidence intervals are constructed to estimate the mean drop in household income in Alberta since the downturn in oil and gas prices. The first is taken from a sample of 50 Calgary households and the second is a sample of 50 taken from Edmonton households. If these two independent intervals are to be compared, which of the following statements is correct?

We are 95% confident that each interval has correctly estimated the mean drop in household income for its respective city.

We are 95% confident that both intervals have correctly estimated the mean drop in household income for its respective city.

We are 95% confident that exactly one of the intervals has correctly estimated the mean drop in household income for its respective city.

None of the above statements are correct.

2.Approximately 500 students take a particular college statistics course each year. As an exercise, each of the 500 students in the class is given a different random sample of the previous year's 500 final grades (in percentages) and asked to construct a 90% interval estimate of the previous year's overall average. Which of the following statements is correct?

About 50 of the sample means will not be found in these confidence intervals.

It is probable that 450 of the confidence intervals will be identical.

About 450 of the confidence intervals will contain the actual overall average for the previous year.

About 450 of the sample means will not be included in the confidence intervals.

3.A new diet program has been developed and is now being tested. The marketing team wishes to focus their marketing campaign around the average (mean) number of kilograms a participant can expect to lose per month under this diet program. To get an estimate of the the mean number of kilograms that the population of participants in this diet can expect to lose, an initial sample of 70 was taken and a 90% confidence interval was constructed. One month later a second sample was taken, this time of 20 participants, and a second 90% confidence interval was constructed. Which confidence interval would you expect to have greater precision (a smaller width) for estimating the population mean?

It is impossible to know as both intervals use the same level of confidence.

I expect the confidence interval based on the sample of 70 data values to be more precise.

I expect the confidence interval based on the sample of 20 data values to be more precise.

I expect both confidence intervals to have the same precision.

4.The marketing team of a new diet program 'The Fat Buster' wishes to compare the expected (mean) monthly weight loss (kgs) to that of the leading program, 'The Blubbernator'. Before launching the campaign, the team will sample 50 test participants from each diet program. A 95% confidence interval will be constructed from each sample to estimate the mean number of kilograms that the population of participants in each diet can expect to lose. If the two intervals are

Fat Buster: 3.3

Blubbernator: 3.1

which of the following would be a legitimate conclusion?

Test results prove the Fat Buster program results in greater average weight loss than the Blubbernator program.

Test results prove the Fat Buster program results in the same weight loss as the Blubbernator program.

Test results prove the Fat Buster program results in greater maximum weight loss than the Blubbernator program.

None of the above can be legitimately claimed.

5.Justin and Hayley are conducting a study of restaurant servers who 'underestimate' their yearly tip totals on their tax returns. They took a random sample of 100 servers and calculated a 95% confidence interval for the proportion of those who admit to underestimating their tip totals. What does a 95% confidence interval tell us in this case? Select thebestanswer

I am 95% confident that this interval includes the sample proportion.

I am 95% confident that the minimum and maximum proportion of servers who admit to underestimating their tip totals will be captured by this interval.

I am 95% confident that this interval includes the true proportion of servers who would admit to underestimating their tip totals.

I am confident that most (95%) of all servers will have underestimated their tips by the mean amount contained within the interval.