BackConstructing a Confidence Interval In Exercises 17–20, you are given the sample mean and the sample standard deviation. Assume the population is normally distributed and use the t-distribution to find the margin of error and construct a 95% confidence interval for the population mean. Interpret the results.
Commute Time In a random sample of eight people, the mean commute time to work was 35.5 minutes and the standard deviation was 7.2 minute
You research prices of cell phones and find that the population mean is $431.61. In Exercise 19, does the t-value fall between -t0.95 and t0.95?
In Exercise 28, the population mean weekly time spent on homework by students is 7.8 hours. Does the t-value fall between -t0.99 and t0.99?
In Exercise 31, the population mean salary is $67,319. Does the t-value fall between -t0.98 and t0.98? (Source: Salary.com)
In Exercises 55–60, find the indicated probabilities and interpret the results.
The mean annual salary for physical therapists in the United States is about $87,000. A random sample of 50 physical therapists is selected. What is the probability that the mean annual salary of the sample is (b) more than $85,000? Assume sigma = $10,500.
In Exercises 15 and 16, find the t-value for the given values of xbar, μ, s and n.
xbar = 70.3, μ = 64.8, s = 7.1, n = 16
In Exercises 13 and 14, use the confidence interval to find the margin of error and the sample mean.
(14.7, 22.1)
In Exercises 9–12, construct the indicated confidence interval for the population mean μ using the t-distribution. Assume the population is normally distributed.
c = 0.99, xbar = 24.7, s = 4.6, n = 50
In Exercises 9–12, construct the indicated confidence interval for the population mean μ using the t-distribution. Assume the population is normally distributed.
c = 0.98, xbar = 4.3, s = 0.34, n = 14
In Exercises 7 and 8, find the margin of error for the values of c, s, and n.
c = 0.99, s = 3, n = 6
In Exercises 7 and 8, find the margin of error for the values of c, s, and n.
c = 0.95, s = 5, n = 16
Describe how the t-distribution curve changes as the sample size increases.
Finite Population Correction Factor In Exercises 57 and 58, use the information below.
In this section, you studied the construction of a confidence interval to estimate a population mean. In each case, the underlying assumption was that the sample size n was small in comparison to the population size N. When n ≥ 0.05N however, the formula that determines the standard error of the mean needs to be adjusted, as shown below.
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Recall from the Section 5.4 exercises that the expression sqrt[(N-n)/(n-1)] is called a finite population correction factor. The margin of error is
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Use the finite population correction factor to construct each confidence interval for the population mean.
c. c = 0.95, xbar = 40.3, σ = 0.5, N = 300, n = 68.
Finite Population Correction Factor In Exercises 57 and 58, use the information below.
In this section, you studied the construction of a confidence interval to estimate a population mean. In each case, the underlying assumption was that the sample size n was small in comparison to the population size N. When n ≥ 0.05N however, the formula that determines the standard error of the mean needs to be adjusted, as shown below.
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Recall from the Section 5.4 exercises that the expression sqrt[(N-n)/(n-1)] is called a finite population correction factor. The margin of error is
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Use the finite population correction factor to construct each confidence interval for the population mean.
a. c = 0.99, xbar = 8.6, σ = 4.9, N = 200, n = 25.
When all other quantities remain the same, how does the indicated change affect the minimum sample size requirement? Explain.
b. Increase in the error tolerance