Question

Use StatCrunch for each problem. Write which StatCrunch menu option you used, and give either both the test-statistic and the p-value, or else the confidence interval.

CAUTION: Some of the problems may involve categorical variables and proportions, rather than the newer material on numerical variables and means!

1. Give a 99% confidence interval for the mean price of new mid-size cars, based on a sample of 12 mid-size cars that has a mean of $21,350 and a standard deviation of $2010.

2. Here are the ages for a sample of employees at a large company.

40 39 48 24 25 58 36 52

a. Report a 99% confidence interval.

b. Interpret the interval in context by finishing the sentence: I am 99% confident that…

3. A random sample of college students found that 210 of the 305 upperclassmen were satisfied with their academic experience, while 115 out of 285 underclassmen were satisfied with their academic experience. Is there a significant difference between the two groups? Carry out a hypothesis test to answer the question.

4. For the data in question #3, give a 95% confidence interval for the difference in the population proportions for the two groups.

Answer 1

1. 99% Confidence Interval: 21350 ± 1490
(19900 to 22800)
Margin of Error: 1490
"With 99% confidence the population mean is between 19900 and 22800, based on only 12 samples."

2. (a)

99% Confidence Interval: 40.3 ± 11
(29.3 to 51.3)

(b) "I am 99% confident that the population mean is between 29.3 and 51.3, based on only 8 samples."
Margin of Error: 11.02
Sample Size: 8
Sample Mean: 40.3
Standard Deviation: 12.1

3.

H0: p1 - p2 = 0, where p1 is the proportion from the first population and p2 the proportion from the second.

Equation

p1=0.6885 p2=0.4035

n1=305 n2=285

So, The Z-Score is 6.9547. The p-value is 0. The result is significant at p <0.05

z-critical=1.96 z-score>z critical So reject null. So significant difference

4.

Define:

Define:

The 100(1-?)% confidence interval with continuity correction is defined as:

d Difference between p₂ and p₁=  -0.285

Lower Lower C.I. = -0.3655

Upper   Upper C.I. = -0.2045