1) Twenty-eight small communities in Connecticut (population near 10,000 each) gave an average of x = 138.5 reported cases of larceny per year. Assume that σ is known to be 42.7 cases per year.
(a) Find a 90% confidence interval for the population mean annual number of reported larceny cases in such communities. What is the margin of error? (Round your answers to one decimal place.)
lower limit
upper limit
margin of error
(b) Find a 95% confidence interval for the population mean annual number of reported larceny cases in such communities. What is the margin of error? (Round your answers to one decimal place.)
lower limit
upper limit
margin of error
(c) Find a 99% confidence interval for the population mean annual number of reported larceny cases in such communities. What is the margin of error? (Round your answers to one decimal place.)
lower limit
upper limit
margin of error
2) What price do farmers get for their watermelon crops? In the third week of July, a random sample of 38 farming regions gave a sample mean of x = $6.88 per 100 pounds of watermelon. Assume that σ is known to be $1.90 per 100 pounds.
(a) Find a 90% confidence interval for the population mean price (per 100 pounds) that farmers in this region get for their watermelon crop. What is the margin of error? (Round your answers to two decimal places.)
lower limit mce_markernbsp;
upper limit mce_markernbsp;
margin of error mce_markernbsp;
(b) Find the sample size necessary for a 90% confidence level with maximal error of estimate E = 0.31 for the mean price per 100 pounds of watermelon. (Round up to the nearest whole number.)
farming regions
(c) A farm brings 15 tons of watermelon to market. Find a 90% confidence interval for the population mean cash value of this crop. What is the margin of error? Hint: 1 ton is 2000 pounds. (Round your answers to two decimal places.)
lower limit mce_markernbsp;
upper limit mce_markernbsp;
margin of error mce_markernbsp;
3) Let x be a random variable that represents hemoglobin count (HC) in grams per 100 milliliters of whole blood. Then x has a distribution that is approximately normal, with population mean of about 14 for healthy adult women. Suppose that a female patient has taken 10 laboratory blood tests during the past year. The HC data sent to the patient's doctor are as follows.
15 17 16 20 13 12 15 18 15 10
(i) Use a calculator with sample mean and standard deviation keys to find x and s. (Round your answers to two decimal places.)
x =
s =
(ii) What is the value of the sample test statistic? (Round your answer to three decimal places.)
(iii) Find the P-value. (Round your answer to four decimal places.)
4) Tree-ring dating from archaeological excavation sites is used in conjunction with other chronologic evidence to estimate occupation dates of prehistoric Indian ruins in the southwestern United States. Suppose it is thought that a certain pueblo was occupied around 1290 A.D. (based on evidence from potsherds and stone tools). The following data give tree-ring dates (A.D.) from adjacent archaeological sites:
1189 1267 1268 1275 1275 1271 1272 1316 1317 1230
(i) Use a calculator with sample mean and standard deviation keys to find x and s. (Round your answers to one decimal place.)
x = A.D.
s = yr
(ii) What is the value of the sample test statistic? (Round your answer to three decimal places.)
(iii) Find the P-value. (Round your answer to four decimal places.)
5)A national newspaper reported that the state with the longest mean life span is Hawaii, where the population mean life span is 78 years. A random sample of 20 obituary notices in the Honolulu Advertizer gave the following information about life span (in years) of Honolulu residents.
72 68 81 93 56 19 78 94 83 84
77 69 85 97 75 71 86 47 66 27
(i) Use a calculator with sample mean and standard deviation keys to find x and s. (Round your answers to two decimal places.)
x = yr
s = yr
(ii) Assuming that life span in Honolulu is approximately normally distributed, does this information indicate that the population mean life span for Honolulu residents is less than 78 years? Use a 1% level of significance.
What is the level of significance?
What is the value of the sample test statistic? (Round your answer to three decimal places.)
(iii) Find the P-value. (Round your answer to four decimal places.)