Exam 10: One-Sample Tests of Hypothesis

A manufacturer claims that less than 1% of all its products do not meet the minimum government standards. A survey of 500 products revealed that 10 did not meet the standard. If the computed z-statistic is -1.960 and the level of significance is 0.01, your decision would be _______________.

How is the significance level related to the probability of a Type I error?

What are the critical values for a two-tailed test with a 0.01 level of significance when n is large and the population standard deviation is known?

The average cost of tuition and room and board at a small private liberal arts college is reported to be $8,500 per term, but a financial administrator believes that the average cost is higher. A study conducted using 350 small liberal arts colleges showed that the average cost per term is $8,745. The population standard deviation is $1,200. Let α = 0.05. What are the null and alternative hypotheses for this study?

In hypothesis testing, what is the level of significance?

It is claimed that in a bushel of peaches, less than 10% are defective. A sample of 400 peaches is examined and 50 are found to be defective. What is the critical value for α = 0.025?

If we reject the null hypothesis, what can we conclude subject to the probability, α?

The number of trials and the population proportion are respectively represented by what symbols?

A random sample of 400 families who planned to buy a vacation residence revealed that 228 families want to buy a condominium in Florida. What is the test statistic to evaluate the statement that 55% of those families who plan to purchase a vacation residence in Florida want a condominium?

How is a significance level determined and how is it related to Type I error?

In hypothesis testing, the probability of a Type I error is also called the _________________.

Assuming that the null hypothesis is true, a p-value is the probability of observing a sample value greater than and/or less than an observed sample observation.

For a two-tailed hypothesis test, the computed test statistic is z = 2.65. What is the p-value?

A Type II error is the probability of rejecting the null hypothesis when it is actually true.

Based on the Nielsen ratings, the local CBS affiliate claims its 11 p.m. newscast reaches 41% of the viewing audience in the area. In a survey of 100 viewers, 36% indicated that they watch the late evening news on this local CBS station. What is the null hypothesis?

A hypothesis regarding the weight of newborn infants at a community hospital is that the mean is 6.6 pounds. A sample of seven infants is randomly selected and their weights at birth are recorded as 9.0, 7.3, 6.0, 8.8, 6.8, 8.4, and 6.6 pounds. If α = 0.05, what is the critical t value?

The mean length of a candy bar is 43 millimeters. There is concern that the settings of the machine cutting the bars have changed. Test the claim at the 0.02 level that there has been no change in the mean length. The alternate hypothesis is that there has been a change. Twelve bars (n = 12) were selected at random and their lengths recorded. The lengths are (in millimeters) 42, 39, 42, 45, 43, 40, 39, 41, 40, 42, 43, and 42. The mean of the sample is 41.5 and the standard deviation is 1.784. Computed t = -2.913. Has there been a statistically significant change in the mean length of the bars?

A manufacturer claims that less than 1% of all its products do not meet the minimum government standards. A survey of 500 products revealed that 10 did not meet the standard. If the z-statistic is -2.58 and the level of significance is 0.02, your decision would be __________.

Based on the Nielsen ratings, the local CBS affiliate claims its 11 p.m. newscast reaches 41% of the viewing audience in the area. In a survey of 100 viewers, 36% indicated that they watch the late evening news on this local CBS station. What is the sample proportion?

For a null hypothesis, H₀: µ = 4,000, if the 1% level of significance is used and the z-test statistic is +6.00, what is our decision regarding the null hypothesis?