Exam 9: One-Sample Tests of a Hypothesis

i. To prevent bias, the level of significance is selected before setting up the decision rule and sampling the population. Ii) The fifth and final step in testing a hypothesis is taking a sample and, based on the decision rule, deciding if the null hypothesis should be rejected. Iii) When the null hypothesis is not rejected, the conclusion is that our sample data does not allow us to reject the null hypothesis.

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. What is the sample proportion?

A manufacturer of stereo equipment introduces new models in the fall. Retail dealers are surveyed immediately after the Christmas selling season regarding their stock on hand of each piece of equipment. It has been discovered that unless 40% of the new equipment ordered by the retailers in the fall had been sold by Christmas, immediate production cutbacks are needed. The manufacturer has found that contacting all of the dealers after Christmas by mail is frustrating as many of them never respond. This year 80 dealers were selected at random and telephoned regarding a new receiver. It was discovered that 38% of those receivers had been sold. Since 38% is less than 40%, does this mean that immediate production cutbacks are needed or can this difference of 2 percentage points be attributed To sampling? Test at the 0.05 level. Computed z = -0.37.

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 16 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 claim that "40% of those persons who retired from an industrial job before the age of 60 would return to work if a suitable job was available," is to be investigated at the 0.02 level of risk. If 74 out of the 200 workers sampled said they would return to work, what is our decision?

If α = 0.05, what is the probability of making a Type I error?

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. What is the z-statistic?

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.

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?

What does z equal for an α = 0.01 and a lower level test?

The mean gross annual incomes of certified tack welders are normally distributed with the mean of $50,000 and a standard deviation of $4,000. The ship building association wishes to find out whether their tack welders earn more or less than $50,000 annually. The alternate hypothesis is that the mean is not $50,000. Which of the following is the alternate hypothesis?

What is the 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?

What is the critical value for a one-tailed hypothesis test in which a null hypothesis is tested at the 5% level of significance based on a sample size of 25?

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 16 items results in a sample mean of 17.1 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 critical z-value for a one-tailed lower test at the 1% level of risk?

i. If we do not reject the null hypothesis based on sample evidence, we have proven beyond doubt that the null hypothesis is true. 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 gross annual incomes of certified tack welders are normally distributed with the mean of $50,000 and a standard deviation of $4,000. The ship building association wishes to find out whether their tack welders earn more or less than $50,000 annually. The alternate hypothesis is that the mean is not $50,000. Which of the following is the alternate hypothesis?

i. The level of significance is the risk we assume of rejecting the null hypothesis when it is actually true. ii. There is only one level of significance that is applied to all studies involving sampling. Iii) The researcher must decide on the level of significance before formulating a decision rule and collecting sample data.

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