Exam 9: One-Sample Tests of Hypothesis

A manufacturer wants to increase the absorption capacity of a sponge. Based on past data, the average sponge could absorb 103.5ml. After the redesign, the absorption amounts of a sample of sponges were (in millilitres): 121.3, 109.2, 97.6, 103.5, 112.4, 115.3, 106.5, 112.4, 118.3, and 115.3. What is the decision rule at the 0.01 level of significance to test if the new design increased the absorption amount of the sponge?

The Jamestown Steel Company manufactures and assembles desks and other office equipment at several plants. The weekly production of the Model A325 desk follows a normal probability distribution, with a mean of 200 and a standard deviation of 16. Recently, due to market expansion, new production methods have been introduced and new employees hired. The vice president of manufacturing would like to investigate whether there has been a change in the weekly production of the Model A325 desk. The mean number of desks produced last year (50 weeks, because the plant was shut down two weeks for vacation) is 203.5. Is the mean number of desks produced different from 200? Test using the.01 significance level.

i. The standard normal distribution is the appropriate distribution when testing a hypothesis about a population proportion. ii. When testing population proportions, the z statistic can be used when np and n(1 - p) are greater than five. iii. To conduct a test of proportions, the assumptions required for the binomial distribution must be met.

The sample size and the population proportion are respectively represented by what symbols?

i. Two types of possible errors always exist when testing hypotheses-a Type I error, in which the null hypothesis is rejected when it should not have been rejected, and a Type II error in which the null hypothesis is not rejected when it should have been rejected. ii. A test statistic is a value determined from sample information collected to test the null hypothesis. iii. The region or area of rejection defines the location of all those values that are so large or so small that the probability of their occurrence under a true null hypothesis is rather remote.

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?

The average cost of tuition, room and board at community colleges is reported to be $8,500 per year with a standard deviation of $1,200, but a financial administrator believes that the average cost is higher. A study conducted using 150 community colleges showed that the average cost per year is $9,000. Let $\alpha$ = 0.05. What is the critical z-value for this test?

What do tests of proportions require of both np and n(1 - p)?

Given: null hypothesis is that the population mean is 16.9 against the alternative hypothesis that the population mean is not equal to 16.9. A random sample of 16 items results in a sample mean of 18.0 and the sample standard deviation is 2.4. It can be assumed that the population is normally distributed. Determine the observed "t" value.

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 81 viewers, 36% indicated that they watch the late evening news on this local CBS station. What is the z test statistic?

The mean weight of newborn infants at a community hospital is said to be 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. Does this sample support the original claim? What is the decision for a statistical significant change in average weights at birth at the 5% level of significance?

A machine is set to fill the small size packages of Smarties candies with 56 candies per bag. A sample revealed: 3 bags of 56, 2 bags of 57, 1 bag of 55, and 2 bags of 58. How many degrees of freedom are there?

A machine is set to fill the small-size packages of Smarties candies with 56 candies per bag. A sample revealed: four bags of 56, two bags of 57, one bag of 55, and two bags of 58. To test the hypothesis that the mean candies per bag is 56, how many degrees of freedom are there?

A restaurant that bills its house account monthly is concerned that the average monthly bill exceeds $200 per account. A random sample of twelve accounts is selected, resulting in a sample mean of $220 and a standard deviation of $12. The t-test is to be conducted at the 5% level of significance. Given the following printout, what can you determine?

i. Two examples of a hypothesis are: 1) mean monthly income from all sources for senior citizens is $841 and 2) twenty percent of juvenile offenders ultimately are caught and sentenced to prison. ii. Hypothesis testing is a procedure based on sample evidence and probability theory to decide whether the hypothesis is a reasonable statement. iii. The test statistic for a problem involving an unknown population standard deviation is the Student's t distribution.

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

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?

A manufacturer claims that less than 1% of all his products do not meet the minimum government standards. A survey of 500 products revealed ten did not meet the standard. If the z-statistic is -1.96 and the level of significance is 0.01, what is your decision?

i. Two examples of a hypothesis are: 1) mean monthly income from all sources for senior citizens is $841 and 2) twenty percent of juvenile offenders ultimately are caught and sentenced to prison. ii. Hypothesis testing is a procedure based on sample evidence and probability theory to decide whether the hypothesis is a reasonable statement. iii. We call a statement about the value of a population parameter a hypothesis.