Critical Values
Find the critical value, tc for c = 0.99 and n = 10.
3.250
Construct the indicated confidence interval for the population mean μ.
c = 0.90, x = 12.3, σ = 1.5, n = 50
12.0 < μ < 12.6
Find the margin of error for the given values of c, σ, and n.
c = 0.95, σ = 677, n = 40
210
When 370 college students were surveyed, 155 said they own their car. Find a point estimate for p, the population proportion of students who own their cars.
0.419
Find the minimum sample size.
c = 0.95, E = 1, σ = 4.8
89
Find the critical value zc that corresponds to a 98% confidence level.
2.33
Construct the indicated confidence interval for the population mean μ using the t-distribution.
c = 0.99, x = 22.4, s = 3.8, n = 19
19.9 < μ < 24.9
Find the value of E, the margin of error, for c = 0.90, n = 16 and s = 2.4.
1.05
In a survey of 2480 golfers, 15% said they were left-handed. The surveyʹs margin of error was 3%. Construct a confidence interval for the proportion of left-handed golfers.
0.12 < p < 0.18
A researcher at a major hospital wishes to estimate the proportion of the adult population of the United States that has high blood pressure. How large a sample is needed in order to be 99% confident that the sample proportion will not differ from the true proportion by more than 6%?
461
Find the critical value, tc for c = 0.90 and n = 15.
1.761
A group of 40 bowlers showed that their average score was 192. Assume the population standard deviation is 8. Find the 95% confidence interval of the mean score of all bowlers.
189.5 < μ < 194.5
Find the value of E, the margin of error, for c = 0.90, p̂= 0.25, and n = 56.
0.095 or 0.10
A survey of 280 homeless persons showed that 63 were veterans. Construct a 90% confidence interval for the proportion of homeless persons who are veterans.
0.184 < p < 0.266
A researcher wishes to estimate the number of households with two cars. How large a sample is needed in order to be 99% confident that the sample proportion will not differ from the true proportion by more than 3%? A previous study indicates that the proportion of households with two cars is 25%
1382
Find the critical values, X2R and X2L , for c = 0.95 and n = 12.
3.816 and 21.920
Using the t-distribution, construct a 90% confidence interval for the population mean, μ. Assume the population has a normal distribution. A sample of 15 randomly selected students has a grade point average of 2.86 with a standard deviation of 0.78.
2.51 < μ < 3.21
The Federal Bureau of Labor Statistics surveyed 50,000 people and found the unemployment rate to be 5.8%. Find the margin of error for the population proportion using a 95% confidence.
0.002 or 0.2%
The mean replacement time for a random sample of 12 microwave ovens is 8.6 years with a standard deviation of 3.8 years. Construct the 98% confidence interval for the population variance, σ2.
6.4 < σ2 < 52.0
The standard IQ test has a mean of 97 and a standard deviation of 17. We want to be 95% certain that we are within 5 IQ points of the true mean. Determine the required sample size.
45