How much do wild mountain lions weigh? Suppose that in a certain region adult wild mountain lions (18 months or older) captured and released for the first time gave the following weights (pounds):
60 100 125 126 63 64
For these sample data, the mean is 89.7 pounds and the sample standard deviation is s 31.4 pounds. Find an 80% confidence interval for the population average weight of all adult mountain lions in the specified region. Round your answer to two decimal places.
a. 70.8 pounds to 101.1 pounds
b. 67.6 pounds to 101.1 pounds
c. 56.9 pounds to 101.1 pounds
d. 70.8 pounds to 108.6 pounds
e. 67.6 pounds to 108.6 pounds
Question 2
True or False? As the degrees of freedom increase, the Student’s t distribution becomes more like the standard normal distribution.
True
False .
Question 3
The price of a share of stock divided by the company’s estimated future earnings per share is called the P/E ratio. High P/E ratios usually indicate “growth” stocks, or maybe stocks that are simply overpriced. Low P/E ratios indicate “value” stocks or bargain stocks. A random sample of 10 of the largest companies in a country gave the following P/E ratios.
14 36 17 13 58 62 70 42 55 77
For these sample data, the mean is 44.4 and the sample standard deviation iss 23.7. Find a 95% confidence interval for the P/E population mean of all large companies of that country. Round your answer to one decimal place.
a. 27.4 to 53.6
b. 27.5 to 53.6
c. 19.8 to 53.6
d. 27.4 to 61.4
e. 27.5 to 61.4
Question 4
Suppose thirty communities gave an average of = 142.6 reported cases of larceny per year. Assume that is known to be 45.8 cases per year. Find a 75%, 85%, and 90% confidence interval for the population mean annual number of reported larceny cases in such communities. Compare the lengths of the confidence intervals. As the confidence levels increase, do the confidence intervals increase in length?
a. The 75% confidence level has a confidence interval length of 105.3; the 85% confidence level has a confidence interval length of 131.9; and the 90% confidence level has a confidence interval length of 150.7. As the confidence level increases, the confidence interval length increases.
b. The 75% confidence level has a confidence interval length of 150.7; the 85% confidence level has a confidence interval length of 131.9; and the 90% confidence level has a confidence interval length of 105.3. As the confidence level increases, the confidence interval lengths decreases.
c. The 75% confidence level has a confidence interval length of 5.0; the 85% confidence level has a confidence interval length of 4.4; and the 90% confidence level has a confidence interval length of 3.5. As the confidence level increases, the confidence interval length decreases.
d. The 75% confidence level has a confidence interval length of 3.5; the 85% confidence level has a confidence interval length of 4.4; and the 90% confidence level has a confidence interval length of 5.0. As the confidence level increases, the confidence interval lengths increases.
e. The 75% confidence level has a confidence interval length of 19.2; the 85% confidence level has a confidence interval length of 24.1; and the 90% confidence level has a confidence interval length of 27.5. As the confidence level increases, the confidence interval lengths increases.
Question 5
What price do farmers get for their watermelon crops? In the third week of July, a random sample of 54 farming regions gave a sample mean of = $6.3 per 100 pounds of watermelon. Assume that is known to be $1.98 per 100 pounds. Find the margin of error for 99% confidence level for the population mean price (per 100 pounds) that farmers in this region get for their watermelon crop. Round your answer to the nearest cent.
Answer a. $13.47 per 100 pounds
b. $0.09 per 100 pounds
c. $0.19 per 100 pounds
d. $0.70 per 100 pounds
e. $0.27 per 100 pounds
Question 6
True or false? The point estimate for the population mean of an x distribution is , computed from a random sample of the x distribution.
True
False
Question 7
Total plasma volume is important in determining the required plasma component in blood replacement theory for a person undergoing surgery. Plasma volume is influenced by the overall health and physical activity of an individual. Suppose that sample of some male firefighters are tested and that they have a plasma volume sample mean of = 36.5 ml/kg (milliliters of plasma per kilogram body weight). Assume that = 7.60 ml/kg for the distribution of blood plasma. Find the smallest sample size necessary for a 98% confidence level with maximal error estimate E = 3.1.
a. 6
b. 29
c. 3
d. 37
e. 33
Question 8
Answer the question Yes or No. Sam computed a 90% confidence interval for from a specific random sample of size n. He claims that at the 90% confident level, his confidence interval does not contain . Is this claim correct?
a. Yes
b. No
Question 9
Consider a 95% confidence interval for . Assume is not known. For which sample size, n = 18 or n = 24, is the confidence interval longer?
a. 24
b. 18
Question 10
Total plasma volume is important in determining the required plasma component in blood replacement theory for a person undergoing surgery. Plasma volume is influenced by the overall health and physical activity of an individual. Suppose that sample of 61 male firefighters are tested and that they have a plasma volume sample mean of = 39.5 ml/kg (milliliters of plasma per kilogram body weight). Assume that = 7.50 ml/kg for the distribution of blood plasma. Find the margin of error for 98% confidence level of the population mean blood plasma volume in male firefighters. Round your answer to two decimal places.
Answer a. 0.29 ml/kg
b. 2.24 ml/kg
c. 51.90 ml/kg
d. 0.34 ml/kg
e. 0.94 ml/kg
Question 11
Total plasma volume is important in determining the required plasma component in blood replacement theory for a person undergoing surgery. Plasma volume is influenced by the overall health and physical activity of an individual. Suppose that sample of 50 male firefighters are tested and that they have a plasma volume sample mean of = 38.5 ml/kg (milliliters of plasma per kilogram body weight). Assume that = 7.70 ml/kg for the distribution of blood plasma. Find the 95% confidence interval of the population mean blood plasma volume in male firefighters. Round your answer to two decimal places.
a. 37.47 ml/kg to 39.53 ml/kg
b. 36.87 ml/kg to 35.87 ml/kg
c. 36.37 ml/kg to 40.63 ml/kg
d. 38.13 ml/kg to 38.87 ml/kg
e. 38.20 ml/kg to 38.80 ml/kg
Question 12
Suppose a certain species bird has an average weight of = 3.40 grams. Based on previous studies, we can assume that the weights of these birds have a normal distribution with = 0.29 grams. Find the sample size necessary for an 98% confidence level with a maximal error of estimate E = 0.09 for the mean weights of the hummingbirds.
a. 21
b. 155
c. 8
d. 424
e. 57
Question 13
What price do farmers get for their watermelon crops? In the third week of July, a random sample of 51 farming regions gave a sample mean of = $7.08 per 100 pounds of watermelon. Assume that is known to be $1.80 per 100 pounds. Find a 99% confidence interval for the population mean price (per 100 pounds) that farmers in this region get for their watermelon crop. Round your answer to the nearest cent.
a. $6.93 to $5.93 per 100 pounds
b. $6.43 to $7.73 per 100 pounds
c. $6.89 to $7.27 per 100 pounds
d. $6.83 to $7.33 per 100 pounds
e. $6.99 to $7.17 per 100 pounds
Question 14
A random sample of 5830 physicians in Colorado showed that 3175 provided at least some charity care. Let p represent the proportion of all Colorado physicians who provide some charity care. Find a 98% confidence interval for p. Give a brief interpretation of the meaning of the confidence interval you have found. Round your answer to two decimal places.
a. We are 2% confident that the interval from 0.53 to 0.56 is an interval that contains p, the proportion of all Colorado physicians who provide some charity care.
b. We are 98% confident that the interval from 0.02 to 0.53 is an interval that contains p, the proportion of all Colorado physicians who provide some charity care.
c. We are 98% confident that the interval from 0.02 to 0.56 is an interval that contains p, the proportion of all Colorado physicians who provide some charity care.
d. We are 2% confident that the interval from 0.02 to 0.56 is an interval that contains p, the proportion of all Colorado physicians who provide some charity care.
e. We are 98% confident that the interval from 0.53 to 0.56 is an interval that contains p, the proportion of all Colorado physicians who provide some charity care.
Question 15
In a random sample of 508 judges, it was found that 281 were introverts. Let p represent the proportion of all judges who are introverts. Find a point estimate for p. Round your answer to four decimal places.
a. p=0.6762
b. p=0.5531
c. p= 1.0000
d. p= 0.0000
e. p= 0.4469
Question 16
Suppose that out of 15,351 convicts who escaped from U.S. prisons, only 7667 were recaptured. Let p represent the proportion of all escaped convicts who will eventually be recaptured. Find a point estimate for p. Round your answer to four decimal places
a. p= 0.000
b. p= 0.4994
c. p=0.6225
d. p= 0.5006
e. p= 1.0000
Question 17
Suppose that out of 13,351 convicts who escaped from U.S. prisons, only 7367 were recaptured. Let p represent the proportion of all escaped convicts who will eventually be recaptured. Find a 99% confidence interval for p, if a point estimate for p is 0.55. Give a brief interpretation of the meaning of the confidence interval you have found. Round your answer to two decimal places.
a. We are 99% confident that the interval from 0.01 to 0.54 is an interval that contains p, the proportion of all escaped convicts who will eventually be recaptured.
b. We are 99% confident that the interval from 0.01 to 0.56 is an interval that contains p, the proportion of all escaped convicts who will eventually be recaptured.
c. We are 99% confident that the interval from 0.54 to 0.56 is an interval that contains p, the proportion of all escaped convicts who will eventually be recaptured.
d. We are 1% confident that the interval from 0.01 to 0.56 is an interval that contains p, the proportion of all escaped convicts who will eventually be recaptured.
e. We are 1% confident that the interval from 0.54 to 0.56 is an interval that contains p, the proportion of all escaped convicts who will eventually be recaptured.
Question 18
In a random sample of 67 professional actors, it was found that 50 were extroverts. Let p represent the proportion of all actors who are extroverts. Find a point estimate for p.
a. 0.373
b. 0.746
c. 0.627
d. 17
e. 50
Question 19
Suppose you want to conduct a survey to determine the proportion of people who favor a proposed tax policy. How does decreasing the sample size affect the size of the margin of error?
a. Decreasing the sample size decreases the size of the margin of error.
b. Decreasing the sample size increases the size of the margin of error.
Question 20
In a random sample of 61 professional actors, it was found that 53 were extroverts. Find a 95% confidence interval for p.
a. 0.782 to 1.433
b. 0.797 to 0.955
c. 0.797 to 0.941
d. 0.782 to 0.941
e. 0.782 to 0.955