Exam 10: One-Sample Tests of Hypothesis

A consumer products company wants to increase the absorption capacity of a sponge. Based on past data,the average sponge could absorb 3.5 ounces. After the redesign,the absorption amounts of a sample of sponges were (in ounces): 4.1,3.7,3.3,3.5,3.8,3.9,3.6,3.8,4.0,and 3.9. At the 0.01 level of significance,what is the decision rule to test if the new design increased the absorption of the sponge?

Using a 5% level of significance and a sample size of 25,what is the critical t-value for a null hypothesis,H₀: µ ≤ 100?

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

An example of a hypothesis is: A person is innocent until proven guilty.

The mean annual incomes of certified welders are normally distributed with the 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. A sample of 100 welders is taken and the mean annual income of the sample is $50,350. If the level of significance is 0.10,what conclusion should be drawn?

If the null hypothesis is false and the researchers do not reject it,a Type I error has been made.

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?

What is a Type II error?

Consider a right-tailed test (upper tail)and a sample size of 40 at the 95% confidence level. The value of t is ________.

A p-value is a probability.

The mean annual incomes of certified welders are normally distributed with the 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. A sample of 100 welders is taken and the mean annual income of the sample is $50,350. If the level of significance is 0.05,what conclusion should be drawn?

The average cost of tuition plus room and board for 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 is the critical z-value for this test?

What is another name for the alternate 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. What is the sample standard deviation?

Which symbol represents a test statistic used to test a hypothesis about a population mean?

A manufacturer wants to increase the shelf life of a line of cake mixes. Past records indicate that the average shelf life of the mix is 216 days. After a revised mix has been developed,a sample of nine boxes of cake mix gave these shelf lives (in days): 215,217,218,219,216,217,217,218,and 218. Using α = 0.025,has the shelf life of the cake mix increased?

What statement do we make that determines if the null hypothesis is rejected?

In hypothesis testing,what is the level of significance?

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?

If the null hypothesis is µ ≥ 200,then a two-tail test is being conducted.