Use Table C or software to find

(a) the critical value for a one-sided test (in the greater than direction) with level a= 0.05 based on the t(5) distribution.

(b) the critical value for a 98% confidence interval based on the t(21) distribution.

Because the t procedures are robust, the most important condition for their safe use is that

(a) the population standard deviation a- is known.

(b) the population distribution is exactly Normal.

(c) the data can be regarded as an SRS from the population.

Which of these settings does not allow use of a matched pairs t procedure?

(a) You interview both the husband and the wife in 64 married couples and ask each about their ideal number of children.

(b) You interview a sample of 64 unmarried male students and another sample of 64 unmarried female students and ask each about their ideal number of children.

(c) You interview 64 female students in their freshman year and again in their senior year and ask each about their ideal number of children.

Which of the following would be most worrisome for the validity of the confidence interval you calculated in the previous exercise?

(a) The presence of a clear outlier in the raw data

(b) A mild skew in the stemplot of the raw data

(c) Not knowing the population standard deviation s

Data on the blood cholesterol levels of 24 rats in mg/di give x = 85 ands = 12. A 95% confidence interval for the mean blood cholesterol of rats under this condition is

(a) 78.7 to91.3.

(b) 79.9 to 90. l.

(c) 80.2 to 89.8.

You have an SRS of 15 observations from a Normally distributed population. What critical value would you use to obtain a 98% confidence interval for the mean u of the population?

(a) 2.326

(b) 2.602

(c) 2.624

The level of nitrogen oxides (NOX) in the exhaust of cars of a particular model varies Normally with mean 0.2 grams per mile (g/mi) and standard deviation 0.05 g/mi. government regulations call for NOX emissions to be no higher than 0.3 g/mi. A company has 25 cars of this model in its fleet. What is the probability that the average NOX level

$$\bar{x}$$

of these cars is above the 0.3 g/mi limit?

You are testing Ho: u = 240 against Ha: u not equal to 240 based on an SRS of 16 observations from a Normal population. The t statistic is t = - 2.112. The P-value for this test

(a) falls between 0.025 and 0.05.

(b) falls between 0.05 and 0.10.

(c) is greater than 0.50.

The P-value for the statistic in the previous exercise

(a) falls between 0.01 and 0.02.

(b) falls between 0.02 and 0.04.

(c) is greater than 0.25.

You are testing Ho: u = 10 against Ha: u smaller than 10 based on an SRS of 20 observations from a Normal population. The t statistic is t = -2.25. The degrees of freedom for this statistic are

(a) 19.

(b) 20.

(c) 21.

You are testing Ho: u = 10 against Ha: u smaller than 10 based on an SRS of 20 observations from a Normal population. The data give x = 8 ands = 4. The value of the t statistic is

(a) -0.5.

(b) -10.

(c) -2.24.

We prefer the t procedures to the z procedures for inference about a population mean because

(a) z can be u ed only for large samples.

(b) z requires that you know the population standard deviation a-.

(c) z requires that you can regard your data as an SRS from the population.

Our bodies have a natural electrical field that is known to help wounds heal. Might higher or lower levels impair healing? The series of experiments introduced in previous examples investigated this question. In one experiment, the two hind limbs of 12 newts were assigned at random to either experimental or control groups. This is a matched pairs design. The electrical field in the experimental limbs was reduced to zero by applying an artificial voltage. The control limbs were not manipulated. Table below gives the rates at which new cells closed a razor cut in each limb.

(a) Make a stemplot or a dotplot of the differences between limbs of the same newt (control limb minus experimental limb). There is a high outlier.

(b) Carry out two t tests to see if the mean healing rate is significantly higher in the control limbs, one including all 12 newts, and another that omits the outlier. What are the test statistics and their P-values? Does the outlier have a strong influence on your conclusion? How to handle outliers is a different challenge in different situations. Refer to the discussion on outliers in previous chapters for an in-depth discussion.

How much more strongly do monkey brains respond to monkey calls than to pure tones? Give a 90% confidence interval to answer this question.