Exam 10: One-Sample Tests of Hypothesis

The alternate hypothesis can be accepted only if the null hypothesis is shown to be _________.

For an alternative hypothesis: µ > 6,700, where is the rejection region for the hypothesis test located?

The mean annual income of certified welders is normally distributed with a mean of $50,000 and a population standard deviation of $2,000. The ship building association wishes to find out whether their welders earn more or less than $50,000 annually. The alternate hypothesis is that the mean is not $50,000. If the level of significance is 0.10, what is the decision rule?

Sales at a fast-food restaurant average $6,000 per day. The restaurant decided to introduce an advertising campaign to increase daily sales. In order to determine the effectiveness of the advertising campaign a sample of 49 days of sales were taken. They found that the average daily sales were $6,400 per day. From past history, the restaurant knew that its population standard deviation is about $1,000. The value of the test statistic is _______.

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. The null hypothesis is ______.

How is a p-value related to the significance level when the null hypothesis is rejected?

The critical t statistic for an alternative hypothesis, H₁: µ > 30, a 1% level of significance, and a sample size of 8 is __________.

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?

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

Records on a fleet of trucks reveal that the average life of a set of spark plugs is normally distributed with a mean of 22,100 miles. The fleet owner purchased 18 sets and found that the sample average life was 23,400 miles; the sample standard deviation was 1,412 miles. To decide if the sample data support the company records that the spark plugs average 22,100 miles, state your decision in terms of the null hypothesis. Use a 0.05 level of significance.

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?

Consider a left-tailed test, where the p-value is found to be 0.10. If the sample size n for this test is 49, then the t statistic will have a value of ________.

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?

The waiting time for patients at a local walk-in health clinic follows a normal distribution with a mean of 15 minutes and a population standard deviation of 5 minutes. The clinic wants to know if the waiting time is less than 15 minutes. The quality-assurance department sampled 50 patients and found that the mean waiting time was 14.25 minutes. For a significance level of 0.05, what is the critical value?

If the null hypothesis is false and the researchers accept it, a _______ error has been made.

Hypothesis testing is a procedure that uses sample evidence and probability theory to decide whether to reject or fail to reject a hypothesis.

As the sample size increases, the curve of the t-distribution approaches the _____________________________.

For a one-tailed hypothesis test, the computed test statistic is z = -2.10. What is the p-value?

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. What is the sample standard deviation?