Question

An article investigated the consumption of caffeine among women. A sample of 49 women were asked to monitor their caffeine intake over the course of one day. The mean amount of caffeine consumed in the sample of women was 242.024 mg with a standard deviation of 222.913 mg. In the article, researchers would like to include a 98% confidence interval.   

• The values below are t critical point corresponding to 90%, 95%, 98%, and 99% confidence. Which critical point corresponds to 98% confidence? SELECT ONE
  • 2.682
  • 1.677
  • 2.407
  • 2.011
• With 98% confidence, we estimate the mean amount of caffeine consumed by women is between ___ mg and ___ mg. (Round the limits of your interval to 4 decimal places.)
• If the level of confidence were changed to 99%, what effect would this have on the width of the calculated confidence interval? SELECT ONE
  • the interval would widen
  • there would be no effect on the interval
  • the interval would narrow

In an upcoming election, voters will be asked to vote on a smoking ban in all bars and restaurants in the county. To help city administrators gauge support for the ban, a random sample of 640 voters is asked their opinion on the smoking ban (favor, neutral, against). Additionally, each voter reports his or her gender. Which of the following inferences would be most appropriate to analyze the data collected? SELECT ONE

• one-sample mean
• chi-square test
• one-sample proportion

A company wants to determine if more than 30% of its customers are female. It will take a random sample of 200 recent customers and record the customer’s gender. Which of the following methods would be most appropriate for analyzing these data?

• chi-square test
• one-sample mean
• one-sample proportion

Answer 1

#1) Given : confidence level = 0.98 , n = 49 , = 242.024 , S = 222.913

α = 1- 0.98 = 0.02 and df = 49 - 1 = 48

=TINV( 0.02, 48)

=2.407

Confidence interval =

t* s

=

242.024 + 2.407 * 222.913 49

Confidence interval is ( 165.387 , 318.661 )

With 98% confidence, we estimate the mean amount of caffeine consumed by women is between 165.387  mg and 318.661 mg.

If the level of confidence were changed to 99%, what effect would this have on the width of the calculated confidence interval?

( As level of confidence increases , t critical value increases , therefore interval would be get wide )

The interval would widen

In an upcoming election, voters will be asked to vote on a smoking ban in all bars and restaurants in the county. To help city administrators gauge support for the ban, a random sample of 640 voters is asked their opinion on the smoking ban (favor, neutral, against). Additionally, each voter reports his or her gender. Which of the following inferences would be most appropriate to analyze the data collected?

( To test the independence between two categorical variable , we use chi square test ).

chi-square test.

A company wants to determine if more than 30% of its customers are female. It will take a random sample of 200 recent customers and record the customer’s gender. Which of the following methods would be most appropriate for analyzing these data?

( here population parameter under study is population proportion )

One-sample proportion.