Exam 8: Large-Sample Estimation

Shuttle Bus Study Narrative An airport bus driver conducted a study to see what proportion of customers use the shuttle bus to get to and from the parking lot. The results of his study are listed below, where B = customer used the bus and W = customer walked. -Refer to Shuttle Bus Study Narrative. Construct a 95% confidence interval for p, the true proportion of all people who used the bus.

Which of the following must hold before one can make use of the standard normal distribution in order to construct a confidence interval estimate for the population proportion p?

A college graduate school administrator is interested in knowing what proportion of applicants would like to be accepted into a particular chemistry program. Of a random sample of 75 applicants, 12 requested entry into the program. Construct a 95% confidence interval for p, the true proportion of all applicants who want acceptance into the program.

The wider the confidence interval, the more likely it is that the interval contains the true value of the population parameter.

The difference between two sample means is an unbiased estimator of the difference between two population means .

Laptop Batteries Narrative A computer laboratory manager was in charge of purchasing new battery packs for her lab of laptop computers. She narrowed her choices to two models that were available for her machines. Since the two models cost about the same, she was interested in determining whether there was a difference in the average time the battery packs would function before needing to be recharged. She took two independent random samples and computed the following summary information: -Refer to Laptop Batteries Narrative. Find a 95% confidence interval for the difference in average functioning time before recharging in the two models.

A dieter believes that the average number of calories in a homemade peanut butter cookie is more than in a store-bought peanut butter cookie. Estimate the difference in the mean calories between the two types of cookies using a 90% confidence interval. The data are = 40, = 180, = 2, = 45, = 179, and = 4, respectively.

In a study of radio listening habits, a station owner would like to estimate the average number of hours that teenagers spend listening each day. If it is reasonable to assume that $\sigma$ = 1.3 hours, how large a sample size is needed to be 90% confident that the sample mean is off by, at most, 30 minutes? Justify your conclusion.

A random sample of 80 jars of grape jelly has a mean weight of 568 g, with a standard deviation of 48.28 g. Construct a 99% confidence interval for $\mu$ , the true weight of a jar of jelly.

A point estimate is a single number that is used as an estimate of a population parameter or population characteristic. It is usually derived from a random sample from the population of interest.

Assume that the population standard deviation of annual incomes of all Manitoba residents is $2500. How many individuals must we include in a simple random sample if we want to be 95% confident that the population mean income lies within $150 of our sample mean income? Justify your conclusion.

Suppose a 90% confidence interval for the mean time it takes to serve a customer at a drive-in bank is 120 seconds to 220 seconds. In repeated sampling, 90% of the intervals constructed using the appropriate formula will contain the actual mean time.

If the population deviation is known and we wish to estimate the population mean with 90% confidence, what is the appropriate critical z-value to use?

Based on the formula we can assume that the point estimate of the population mean will be at the centre of the confidence interval estimate.

Suppose you wish to estimate the difference between two population means when the population variances are known. Which critical value of z can you use to develop the 99% confidence interval estimate?

To what does the term "confidence level" refer?

In estimating the difference between two population means, if a 90% confidence interval estimate includes 0, then we can conclude that there is a 90% chance that the difference between the two population means is 0.

In the formula , the refers to the area in the lower tail or upper tail of the sampling distribution of the sample mean.

Online Time Usage Narrative An Internet server conducted a survey of 400 of its customers and found that the average amount of time spent online was 12.5 hours per week, with a standard deviation of 5.4 hours. -Refer to Online Time Usage Narrative. Construct a 95% confidence interval for the average online time for all users of the particular Internet server.

Shuttle Bus Study Narrative An airport bus driver conducted a study to see what proportion of customers use the shuttle bus to get to and from the parking lot. The results of his study are listed below, where B = customer used the bus and W = customer walked. -Refer to Shuttle Bus Study Narrative. Construct a 90% confidence interval for p, the true proportion of all people who used the bus.