Unit 3

The purpose of a pilot sample is:

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f a hypothesis test for a single population variance is to be conducted, which of the following statements is true

All of the following statements are true

If a manager believes that the required sample size is too large for a situation in which she desires to estimate the mean income of blue collar workers in a state, which of the following would lead to a reduction in sample size?

All options are correct

When testing a two-tailed hypothesis using a significance level of 0.05, a sample size of n = 16, and with the population standard deviation unknown, which of the following is true?

All options are correct

Which of the following statements is true with respect to the t-distribution

All options are correct

A 90% confidence interval is found to be: $6.72 +- 2.38 $4.34 ----- $9.10 Which is the best statement?

Based on the sample data, we are 90% confident the populatuon mean will be between $4.34 and $9.10.

Which distribution is used in testing the hypotheses about the equality of two population variances?

F-distribution

A conclusion to "not reject" the null hypothesis is the same as the decision to "accept" the null hypothesis.

False

A large tire manufacturing company has claimed that its top line tire will average more than 80,000 miles. If a consumer group wished to test this claim, they would formulate the following null and alternative hypotheses: Ho: μ ≥ 80,000 Ha: μ ≠ 80,000

False

A pilot sample is one that is used when a decision maker wishes to get an advance idea of what the mean of the population might be.

False

Hypothesis testing and confidence interval estimation are essentially two totally different statistical procedures and share little in common with each other.

False

If a hypothesis test is conducted for a population mean, a null and alternative hypothesis of the form: Ho: μ = 100 Ha: µ ≠ 100 will result in a one-tailed hypothesis test since the sample result can fall in only one tail.

False

The concept of a confidence interval applies directly when estimating a population mean, but is not appropriate when estimating a population proportion.

False

The following is an appropriate statement of the null and alternate hypotheses for a test of a population mean: Ho: µ < 50 Ha: µ > 50

False

The police chief in a local city claims that the average speed for cars and trucks on a stretch of road near a school is at least 45 mph. If this claim is to be tested, the null and alternative hypotheses are: Ho: µ < 45 Ha: µ ≥ 45

False

When using a 95 percent confidence interval for a mean, the area in the upper tail of the distribution that is outside the interval is 5 percent.

False

A company that makes shampoo wants to test whether the average amount of shampoo per bottle is 16 ounces. The standard deviation is known to be 0.20 ounces. Assuming that the hypothesis test is to be performed using 0.10 level of significance and a random sample of n = 64 bottles, which of the following would be the correct formulation of the null and alternative hypotheses?

Ho: µ = 16 Ha: µ ≠ 16

In a hypothesis test involving a population mean, which of the following would be an acceptable formulation?

Ho: µ ≥ $1,700 Ha: µ < $1,700

An analyst plans to test whether the standard deviation for the time it takes bank tellers to provide service to customers exceeds the standard of 1.5 minutes. The currect null and alterhative hypothesis for this test are:

Ho: σ2 ≤ 2.25 Ha: σ2 > 2.25

The R.D. Wilson Company makes a soft drink dispensing machine that allows customers to get soft drinks from the machine in a cup with ice. When the machine is running properly, the average number of fluid ounces in the cup should be 14. Periodically the machines need to be tested to make sure that they have not gone out of adjustment. To do this, six cups are filled by the machine and a technician carefully measures the volume in each cup. In one such test, the following data were observed: 14.25 13.7 14.02 14.13 13.99 14.04 Which of the following would be the correct null hypothesis if the company wishes to test the machine?

Mu=14

f the variance of the contents of cans of orange juice is significantly more than 0.003, the manager has to order to stop the filling machine. A sample of 26 cans of orange juice showed a standard deviation of 0.06 ounces. Based on the sample and at the 0.05 level of significance, the filling machine should be

Stopped

The reason for using the t-distribution in a hypothesis test about the population mean is:

The pop standard deviation is unknown

A large tire manufacturing company has claimed that its top line tire will average more than 80,000 miles. If a consumer group wished to test this claim, the research hypothesis would be: Ha: µ > 80,000

True

A report in a consumer magazine indicated that with 90 percent confidence, the mean number of hours that a particular brand light bulb lasts is between 900 and 1,100 hours. Based on this, the sample mean that produced this estimate is 1,000 hours

True

A report recently published in a major business periodical stated that the average salary for female managers is less than $50,000. If we were interested in testing this, the following null and alternative hypotheses would be established: Ho: µ ≥ 50,000 Ha: µ < 50,000

True

A two-tailed hypothesis test with alpha = 0.05 is similar to a 95 percent confidence interval.

True

If we are interested in performing a one-tailed, upper-tail hypothesis test about a population variance where the level of significance is .05 and the sample size is n = 20, the critical chi-square value to be used is 30.1435.

True

In a situation where we know the population standard deviation but wish to estimate the population mean using a 90 percent confidence interval, the critical value is z = +-1.645.

True

In hypothesis testing, the null hypothesis should contain the equality sign.

True

Of the two types of statistical errors, the one that decision makers have most control over is Type I error.

True

The higher the level of confidence, the wider the confidence interval must be.

True

The margin of error is one-half the width of the confidence interval.

True

The null and alternate hypotheses must be opposites of each other.

True

When calculating a confidence interval, the reason for using the t-distribution rather than the normal distribution for the critical value is that the population standard deviation is unknown.

True

Whenever possible, in establishing the null and alternative hypotheses, the research hypothesis should be made the alternative hypothesis.

True

When a hypothesis test is to be conducted regarding a population variance, the test statistic will be:

a Χ2 value from the chi-square distribution.

The general format for a confidence interval is:

point estimate +- (critical value)(standard error)

Assume a sample of size n = 12 has been collected. To perform a hypothesis test of a population variance using a 0.05 level of significance, where the null hypothesis is: Ho: σ2 = 25 The upper critical value is 21.92.

true

If an economist wishes to determine whether there is evidence that average family income in a community exceeds $25,000. The best null hypothesis is:

µ ≤ 25,000.