Exam 9: One-Sample Tests of a Hypothesis

From past records it is known that the average life of a battery used in a digital clock is 305 days. The battery life is normally distributed. The battery was recently modified to last longer. A sample of 20 of the modified batteries was tested. It was discovered that the mean life was 311 days and the sample standard deviation was 12 days. We want to test at the 0.05 level of significance whether the modification increases the life of the battery. What is our decision rule?

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.

Test at the 0.01 level the statement that 55% of those families who plan to purchase a vacation residence in Florida want a condominium. The null hypothesis is p = 0.55 and the alternate is p ≠ 0.55. A random sample of 400 families who planned to buy a vacation residence revealed that 228 families want a condominium. What decision should be made regarding the null hypothesis?

i. One assumption in testing a hypothesis about a proportion is that the data collected are the result of counting something. Ii) One assumption in testing a hypothesis about a proportion is that an outcome of an experiment can be classified into two mutually exclusive categories, namely, a success or a failure. Iii) A proportion is a fraction, ratio or probability that gives the part of the population or sample that has a particular trait of interest.

It is claimed that in a bushel of peaches less than ten percent are defective. A sample of 400 peaches is examined and 50 are found to be defective. If α = 0.025, what will be the decision?

i. If the critical values of the test statistic z are ±1.96, they are the dividing points between the areas of rejection and non-rejection. Ii) The probability of a Type I error is also referred to as alpha. Iii) A Type I error is the probability of accepting a true null hypothesis.

Given: null hypothesis is that the population mean is 16.9 against the alternative hypothesis that the population mean is not equal to 6.9. A random sample of 25 items results in a sample mean of 17.8 And the sample standard deviation is 2.4. It can be assumed that the population is normally distributed. Determine the observed "t" value.

The dean of a business school claims that the average starting salary of its graduates is more than $50,000. It is known that the population standard deviation is $10,000. Sample data on the starting salaries of 20 randomly selected recent graduates yielded a mean of $55,000. What is the value of the sample test statistic?

i. The probability of a Type I error is also referred to as alpha. ii. A Type I error is the probability of accepting a true null hypothesis. iii. A Type I error is the probability of rejecting a true null hypothesis.

i. An alternate hypothesis is a statement about a population parameter that is accepted when the null hypothesis is rejected. Ii) The level of significance is the risk we assume of rejecting the null hypothesis when it is actually true. Iii) The researcher must decide on the level of significance before formulating a decision rule and collecting sample data.

i. A sample proportion is found by dividing the number of successes in the sample by the number sampled. Ii) The standard normal distribution is the appropriate distribution when testing a hypothesis about a population proportion. Iii) When testing population proportions, the z statistic can be used when np and n(1 - p) are greater than five.

Based on the Nielsen ratings, the local CBS affiliate claims its 11:00 PM 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 your decision if α = 0.01?

Given: null hypothesis is that the population mean is 16.9 against the alternative hypothesis that the population mean is not equal to 6.9. A random sample of 25 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.

What is the level of significance?

The mean weight of newborn infants at a community hospital 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. Does this sample support the original claim? What is the alternate 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?

If the alternative hypothesis states that μ > 6,700, what is the rejection region for the hypothesis test?

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. At the 0.025 level, has the shelf life of the cake mix increased?

A random sample of size 15 is selected from a normal population. The population standard deviation is unknown. Assume that a two-tailed test at the 0.10 significance level is to be used. For what value of t will the null hypothesis be rejected?

The mean weight of newborn infants at a community hospital 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. 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?