Exam 9: One-Sample Tests of 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. If α = 0.05, what is the critical t value?

What is the critical z-value for a one-tailed lower test at the 1% level of risk?

Which of the following is NOT one of the five steps in the hypothesis testing procedure?

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.

A nationwide survey of college students was conducted and found that students spend two hours per class hour studying. A professor at your school wants to determine whether the time students spend at your school is significantly different from the two hours. A random sample of fifteen statistics students is carried out and the findings indicate an average of 1.75 hours with a standard deviation of 0.24 hours. Test at the 5% level of significance.

The printout below refers to the weekly closing stock prices for Air Canada on 20 randomly selected weeks in 2000. Using a 5% level of significance, can you say that the average Air Canada stock price was different from $19.50?

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?

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?

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?

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 critical value for α = 0.025?

The average cost of tuition, room and board at community colleges is reported to be $8,500 per year, 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 with a standard deviation of $1,200. Let α = 0.05. Given the z-statistic is 5.1, what is our decision about the average cost?

To conduct a test of hypothesis with a small sample, we need to be able to make the following assumption that:

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. What are the degrees of freedom associated with this claim?

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.

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.

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 the critical value if the level of significance is 0.10?

i. To prevent bias, the level of significance is selected before setting up the decision rule and sampling the population. Ii) The level of significance is the probability that a true hypothesis is rejected. Iii) 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.

i. 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. Ii) When the null hypothesis is not rejected, the conclusion is that our sample data does not allow us to reject the null hypothesis. Iii) The level of significance is selected after setting up a decision rule and sampling the population.

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) To conduct a test of proportions, the assumptions required for the binomial distribution must be met.

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. What is the sample variance?