1. A coin-operated drink machine was designed to discharge a mean of ounces of coffee per cup. In a test of the machine, the discharge amounts in randomly chosen cups of coffee from the machine were recorded. The sample mean and sample standard deviation were ounces and ounces, respectively. If we assume that the discharge amounts are normally distributed, is there enough evidence, at the level of significance, to conclude that the true mean discharge, , differs from ounces?
Perform a two-tailed test. Then fill in the table below.
Carry your intermediate computations to at least three decimal places and round your answers as specified in the table. (If necessary, consult a list of formulas.)
2
It was claimed recently that more than of high school students in the United States use computers for educational purposes. We wish to examine this claim. We choose a random sample of U.S. high school students and find that of these students use computers for educational purposes. Based on this, can we conclude, at the level of significance, that more than of high school students in the United States use computers for educational purposes? In your answers, denote the proportion of all U.S. high school students who happen to use computers for educational purposes by. Perform a one-tailed test. Then fill in the table below.Carry your intermediate computations to at least three decimal places and round your answers as specified in the table. (If necessary, consult a list of formulas.)
Can we conclude that more than 60% of high school student in the u.s use computers for educational purposes? Yes or NO
3
An industrial plant wants to determine which of two types of fuel, electric or gas, is more cost efficient (measured in cost per unit of energy). Independent random samples were taken of plants using electricity and plants using gas. These samples consisted of plants using electricity, which had a mean cost per unit of and standard deviation of, and plants using gas, which had a mean of and standard deviation of. Assume that the populations of costs per unit are normally distributed for each type of fuel, and assume that the variances of these populations are equal. Can we conclude, at the level of significance, that the mean cost per unit for plants using electricity, , differs from the mean cost per unit for plants using gas,?
Perform a two-tailed test. Then fill in the table below.
Carry your intermediate computations to at least three decimal places and round your answers as specified in the table
4
At LLD Records, some of the market research of college students is done during promotions on college campuses, while other market research of college students is done through anonymous mail, phone, internet, and record store questionnaires. In all cases, the company solicits an “intent-to-purchase” score from the student, with being the lowest score (“no intent to purchase”) and being the highest score (“full intent to purchase”).
The manager finds the following information for intent-to-purchase scores for a soon-to-be-released CD:
Suppose that the five populations of scores from which these samples were drawn are approximately normally distributed and have the same mean and the same variance.
Answer the following, carrying your intermediate computations to at least three decimal places and rounding your responses to at least one decimal place.
6
A manufacturer claims that the mean lifetime, , of its light bulbs is months. The standard deviation of these lifetimes is months. Ninety bulbs are selected at random, and their mean lifetime is found to be months. Can we conclude, at the level of significance, that the mean lifetime of light bulbs made by this manufacturer differs from months?
Perform a two-tailed test. Then fill in the table below.
Carry your intermediate computations to at least three decimal places, and round your responses as specified in the table. (If necessary, consult a list of formulas.)