1.) Answer each of the following with “point estimate” or “interval estimate” a. A ________________ is an estimate that is a single value, such as using a sample mean to estimate a population mean.
1.) Answer each of the following with “point estimate” or “interval estimate”
a. A ________________ is an estimate that is a single value, such as using a sample
b. A ________________ is an estimate that is a
2.) The mean distance commuted by a sample of 100 people is 25 miles. If the standard deviation of the distance commuted by the population of all commuters is known to be 3 miles, then
a. Find the confidence interval for mean distance commuted by the population of all commuters for a confidence level of 94%
b. Find the confidence interval for mean distance commuted by the population of all commuters for a confidence level of 99%
c. Which interval is wider? Why does this make sense?
3.) How big of a sample would be needed to get a confidence interval for the mean distance commuted by the population of all commuters with a margin of error of 2 miles, and a confidence level of 99%, if the population standard deviation is 3 miles, as above?
4.) The mean length of a sample of 41 fish of a particular species is 21 inches, and the standard deviation of the lengths of the fish in the sample is 2 inches. For a 95% confidence level,
a. What kind of confidence interval should we do (z or t) and why?
b. Find the confidence interval for the mean length of all of the fish of this species.
c. For a sample size of 100 fish, would the confidence interval be narrower, or wider?
5.) The mean height for the population of a species of gorilla is believed to be 70 inches, and the standard deviation for the population of the species of gorilla is known to be 4 inches. A researcher believes that the mean height has changed. He measures a sample of 20 gorillas, and finds the mean height of the gorillas in the sample is 73 inches. For a = 0.10, determine if the mean is different than it was previously.
a. State the null hypothesis and the alternative hypothesis.
b. Is the test left-tailed, right-tailed, or two-tailed?
c. Find the test value
d. Find the critical value or p value
e. Should you reject the null hypothesis
f. Summarize the results
6.) The mean weight for bags of chips is believed to be 16oz. A researcher believes that the actual mean weight is significantly lower than this. The researcher measures the weights of a sample of 31 bags, and finds that the mean of the sample is 15oz, with a sample standard deviation of 4oz. For a = 0.01, determine if the researcher is correct.
a. State the null hypothesis and the alternative hypothesis.
b. Is the test left-tailed, right-tailed, or two-tailed?
c. Find the test value
d. Find the critical value or p value
e. Should you reject the null hypothesis?
f. Summarize the results
7.) It is believed that 30% of drivers in the country make an insurance claim in any given year. An insurance company examines a sample of 200 of its policyholders, and finds that 64 of them made claims last year. Based on this, is there enough evidence to say that the claim rate for this company’s policyholders is higher than for the country overall with a = 0.05?
a. State the null hypothesis and the alternative hypothesis.
b. Is the test left-tailed, right-tailed, or two-tailed?
c. Find the test value
d. Find the critical value or p value
e. Should you reject the null hypothesis?
f. Summarize the results
8. Explain the difference between a Type I error and a Type II error
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