Two sample Tests & Intervals on the

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Two independent random samples of women’s clubs in a particular city are taken in order to determine the average amount of time the members spend volunteering. Fifteen garden club members spent an average of 17.25 days with a standard deviation of 2.4 days. The mean of 12 library members was 16.45 with a standard deviation of 3.6. Construct a 90% confidence interval for the difference in volunteering time.

What kind of Interval? (Use formula)

Result:

Interval:

In a fast food study, a researcher finds that the mean sodium content of 42 Wendy’s fish sandwiches is 1010 milligrams with a standard deviation of 75 mg. The mean sodium content of 39 Long John silver’s fish sandwiches is 1180 mg with a standard deviation of 90 mg. Is there enough evidence fore the researcher to conclude that the Wendy’s fish sandwich has less sodium than the Long John Silver’s fish sandwich?

The guidance dept. wants to see if a new SAT prep program will improve their SAT scores by at least 50 points. Ten members of the junior class were selected. Results are below. Test the claim.

Stud 1 2 3 4 5 6 7 8 9 10

Bef 475 512 494 465 523 560 610 477 501 410

After 500 540 512 530 533 603 691 512 489 458

A real estate agent claims that there is no difference between the mean household incomes of two neighborhoods. The mean income of 12 randomly selected households from the first neighborhood was $32,750 with a standard deviation of $1900. In the second neighborhood, 10 randomly selected households had a mean income of $31,200 with a standard deviation of $1825. Create a 95% confidence interval of the difference in mean household incomes of the two neighborhoods.

In a random sample of 800 US adults, 38% are worried that they are someone in their family will become a victim of terrorism. In another random sample of 1100 US adults taken a month earlier, 42% were worried that someone in their family would become a victim of terrorism. At a 10% level of significance, test the claim that the proportion has changed.

In a survey of 900 US adults in 2008, 468 considered the amount of federal income tax they had to pay to be too high. In a recent year, in a survey of 1027 U.S. adults 472 considered the amount too high. Create a 90% confidence interval of the difference in the proportion who believed that the income tax amount was too high.

Which of the following is true about constructing confidence intervals?

A. The value of the standard error is a function of the sample statistics.

B. The center of the confidence interval is the population parameter.

C. One of the values that affects the width of a confidence interval is the sample size.

D. If the value of the population parameter is know, it is irrelevant to calculate a confidence interval for it.

E. The value of the level of confidence will affect the width of a confidence interval.

The confidence that we feel about a 90%

confidence interval comes from the fact that

A. There is a 90% chance that the population parameter is contained in the confidence interval.

B. There is a 90% chance that the sample statistic is contained in the confidence interval.

C. 90% of confidence intervals constructed around a sample statistic will contain the population parameter.

D. The terms of confidence and probability are interchangeable.

E. The concepts of confidence and probability are synonymous.

If the 95% confidence interval of the proportion of a population is 0.35 ±0.025, which of the following are true?

A. If the sample size were to increase the width of the interval would decrease.

B. An increase in confidence level generally results in an increase in the width of the confidence interval.

C. If one would like a smaller confidence interval, one could increase sample size or decrease the confidence level.

D. This confidence interval could have been calculated after either a sample or a census was conducted.

E. If 1,000 samples of the same size are taken from a population, then approximately 900 will contain the sample mean.

What sample size is needed to be within 2.5% of the true proportion of approval votes at the 98% confidence level.

A preliminary study has indicated that the standard deviation of a population is approximately 7.85 hours. Determine an appropriate sample size if the estimate of the population mean is to be within 2 hours at the 95% confidence level?

Homework

Worksheet Identify the hypothesis Give the formula Give the test statistic Give the p-value State the decision