[1] A survey conducted by the American Automobile Association showed that a family of four spends an average of $215.60 per day while on vacation. Supposea sample of 64 families of four vacationing at Niagara Falls resulted in a sample mean of $252.45 per day and a sample standard deviation of $74.50.
a) If the amount spent by a family of four while vacationing at Niagara Falls is skewed to the right, would you expect the median amount spent to be greater than or less than $252.45? Explain.
b) Is it necessary to assume a normal distribution on the population to estimate the value of the mean spending per day? Explain.
c) Use the sample data to construct a 95% confidence interval estimate for the mean amount spent per day by a family of four visiting Niagara Falls.
d) Based on the confidence interval from part c), does it appear that the population mean amount spent per day by families visiting Niagara Falls differs from the mean reported by the American Automobile Association? Explain.
[2] A nationwide poll claims that the margin of error is no more than 3 percentage points in either direction (i.e., plus or minus) at the 95% confidence level.
a) Verify this claim in a particular case by computing the margin of error of the population proportion p for the case of 309 out of 1105 registered voters reporting that they are in favor of a particular candidate.
b) Find the 95% confidence interval for the percentage of registered voters (p) who favor the candidate as indicated in part a).
[3] In the case of Castenedav. Partida, it was found that during a period of 11 years in Hilda County, Texas, 870 people were selected for grand jury duty, and 39% of them were Americans of Mexican ancestry. Among the people eligible for grand jury duty, 79.1% were Americans of Mexican ancestry. We want to determine ifthe selection process is biased against Americans of Mexican ancestry or not.
a) Construct a 98% confidence interval estimate of the proportion of Americans of Mexican ancestry selected for grand jury during a period of 11 years.
b) Does the jury selection system appear to be fair? Substantiate your response.
[4] A bakery in my neighborhood produces loaves of bread with "1 pound" written on the label. Weights of randomly selected sampled loaves from today's production were recorded below:
|
1.02
|
0.97
|
0.98
|
1.04
|
1.00
|
1.02
|
0.98
|
1.03
|
|
1.03
|
0.99
|
1.02
|
1.06
|
0.95
|
1.01
|
0.97
|
1.02
|
a) If you are to construct a confidence interval estimate for the mean weight of the entire loaves of bread production, what distribution are you going to apply and explain why?
b) Construct a 95% confidence interval estimate for the population mean weight for the entire loaves of bread production.
c) Do you think that the bakery is correct in its label claim?
[5] As the newly hired manager of a company that provides cell phone services, you want to determine the percentage of adults in your state who live in a household with cell phones and no land-line phones. How many adults must you survey? Assume that you want to be 95% confident that the sample percentage is within four percentage points of the true population percentage.
a) Assume that a recent survey suggests that about 8% of adults who live in a household with cell phones and no land-line phones
b) Assume that nothing is known about the percentage of adults who live in a household with cell phones and no land-line phones