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Exam 8: Interval Estimation

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Question 1

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Fifty students are enrolled in an Economics class. After the first examination, a random sample of 5 papers was selected. The grades were 60, 75, 80, 70, and 90. a.Calculate the estimate of the standard error of the mean. b.What assumption must be made before we can determine an interval for the mean grade of all the students in the class? Explain why. c.Assume the assumption of Part b is met. Provide a 90% confidence interval for the mean grade of all the students in the class. d.If there were 200 students in the class, what would be the 90% confidence interval for the mean grade of all the students in the class?

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a.4.79
b.Since the sample is s...

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Question 2

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Whenever the population standard deviation is unknown, which distribution is used in developing an interval estimate for a population mean?

A) standard distribution
B) z distribution
C) binomial distribution
D) t distribution

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Question 3

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A university planner wants to determine the proportion of spring semester students who will attend summer school. She surveys 32 current students discovering that 12 will return for summer school. a.Construct a 90% confidence interval estimate for the proportion of current spring students who will return for summer school. b.With a 0.95 probability, how large of a sample would have to be taken to provide a margin of error of 3% or less?

The manager of University Credit Union (UCU) is concerned about checking account transaction discrepancies. Customers are bringing transaction errors to the attention of the bank's staff several months after they occur. The manager would like to know what proportion of his customers balance their checking accounts within 30 days of receiving a transaction statement from the bank.Using random sampling, 400 checking account customers are contacted by telephone and asked if they routinely balance their accounts within 30 days of receiving a statement. 271 of the 400 customers respond Yes. a. Develop a 95% confidence interval estimate for the proportion of the population of checking account customers at UCU that routinely balance their accounts in a timely manner. b. Suppose UCU wants a 95% confidence interval estimate of the population proportion with a margin of error of E = .025. How large a sample size is needed?

Exhibit 8-2 The manager of a grocery store has taken a random sample of 100 customers. The average length of time it took these 100 customers to check out was 3.0 minutes. It is known that the standard deviation of the checkout time is one minute. -Refer to Exhibit 8-2. If the confidence coefficient is reduced to 0.80, the standard error of the mean

An estimate of a population parameter that provides an interval believed to contain the value of the parameter is known as the

If the margin of error in an interval estimate of $\mu$ is 4.6, the interval estimate equals

A sample of 26 elements from a normally distributed population is selected. The sample mean is 10 with a standard deviation of 4. The 95% confidence interval for $\mu$ is

The general form of an interval estimate of a population mean or population proportion is the _____ plus and minus the _____.

Six hundred consumers were asked whether they would like to purchase a domestic or a foreign automobile. Their responses are given below. Develop a 95% confidence interval for the proportion of all consumers who prefer to purchase domestic automobiles.

In developing an interval estimate of the population mean, if the population standard deviation is unknown

A sample of 16 students from a large university is taken. The average age in the sample was 22 years with a standard deviation of 6 years. Construct a 95% confidence interval for the average age of the population. Assume the population of student ages is normally distributed.

The t value with a 95% confidence and 24 degrees of freedom is

Exhibit 8-2 The manager of a grocery store has taken a random sample of 100 customers. The average length of time it took these 100 customers to check out was 3.0 minutes. It is known that the standard deviation of the checkout time is one minute. -Refer to Exhibit 8-2. The standard error of the mean equals

As the degrees of freedom increase, the t distribution approaches the

A random sample of 25 statistics examinations was taken. The average score in the sample was 76 with a variance of 144. Assuming the scores are normally distributed, the 99% confidence interval for the population average examination score is

From a population that is normally distributed with an unknown standard deviation, a sample of 25 elements is selected. For the interval estimation of $\mu$ , the proper distribution to use is the

In a random sample of 500 college students, 23% say that they read or watch the news every day. Develop a 90% confidence interval for the population proportion. Interpret your results.

The manager of Hudson Auto Repair wants to advertise one price for an engine tune-up, with parts included. Before he decides the price to advertise, he needs a good estimate of the average cost of tune-up parts. A sample of 20 customer invoices for tune-ups has been taken and the costs of parts, rounded to the nearest dollar, are listed below. Provide a 90% confidence interval estimate of the mean cost of parts per tune-up for all of the tune-ups performed at Hudson Auto Repair.

A small stock brokerage firm wants to determine the average daily sales (in dollars) of stocks to their clients. A sample of the sales for 36 days revealed average daily sales of $200,000. Assume that the standard deviation of the population is known to be $18,000. a.Provide a 95% confidence interval estimate for the average daily sale. b.Provide a 97% confidence interval estimate for the average daily sale.