Previous exercise gave the summary data (x = 27.8, s = 32.2 spikes per second) for the baseline activity of a neuron based on 72 separate recordings. Neural activity is expressed in number of action potentials per second and cannot be less than 0. You notice that the standard deviation is larger than the mean. What does it suggest about the shape of the distribution? Is it nonetheless acceptable to calculate a t confidence interval for the population mean? Explain why.

Students in a physiology lab collected 50 wood lice ("pill bugs") from the university grounds. Regard these as a random sample of wood lice on Regard these as a random sample of wood lice on the university grounds. Here are the lengths in millimeters:

11.0 11.1 10.1 10.8 9.2 9.0 11.0 9.5 8.0 14.6

9.1 9.7 12.0 12.5 13.1 11.7 8.1 8.7 11.9 10.3

8.1 8.3 8.2 12.1 12.3 10.9 8.9 7.5 9.0 8.2

8.3 9.0 7.9 10.5 10.0 9.8 8.9 11.0 11.0 10.9

11.0 11.5 11.0 13.9 9.3 8.5 10.2 8.3 9.1 7.0

Verify that there are no outliers in the data. What is a 95% confidence interval for the mean body length in this population?

The alcohol content of wine depends on the grape variety, the way in which the wine is produced from the grapes, the weather, and other influences. Here are data on the percent of alcohol in wine produced from the same grape variety in the same year by 48 winemakers in the same region of Italy:

12.86 12.88 12.81 12.70 12.51 12.60 12.25 12.53 13.49 12.84

12.93 13.36 13.52 13.62 12.25 13.16 13.88 12.87 13.32 13.08

13.50 12.79 13.11 13.23 12.58 13.17 13.84 12.45 14.34 13.48

12.36 13.69 12.85 12.96 13.78 13.73 13.45 12.82 13.58 13.40

12.20 12.77 14.16 13.71 13.40 13.27 13.17 14.13

(a) Make a histogram of the data, using class width 0.25. The shape of the distribution is a bit irregular, but there are no outliers or strong skewness. There is no reason to avoid use oft procedures for n = 48.

(b) Give a 95% confidence interval for the mean alcohol content of wine of this type. (c) Based on your confidence interval, is the mean alcohol content significantly different at the a = 0.05 level from 12%? From 13%?

Sharks. Great white sharks are big and hungry. Here are the lengths in feet of 44 great whites:

(a) Examine these data for shape, center, spread, and outliers. The distribution is reasonably Normal except for one outlier in each direction. Because these are not extreme and preserve the symmetry of the distribution, use of the t procedures is safe with 44 observations.

(b) Give a 95% confidence interval for the mean length of great white sharks. Based on this interval, is there significant evidence at the 5% level to reject the claim "Great white sharks average 20 feet in length"?

(c) Before accepting the conclusions of (b), you need more information about the data. What would you like to know?

A manufacturer of pharmaceutical products analyses a specimen from each batch of product to verify the concentration of the active ingredient. The chemical analysis is not perfectly precise. Repeated measurement on the same specimen give slightly different results. The results of repeated measurements follow a Normal distribution quite closely. The analysis procedure has no bias, so the mean

$$\mu$$

of the population of all measurements is the true concentration in the specimen. From previous experience, the standard deviation of this distribution is known to be

$$sigma = 0.0068$$

grams per liter. The laboratory analyzes each specimen three times and reports the mean result. Three analyzes of one specimen give concentrations

$$\\ 0.8403 \ \ \ \ 0.8363 \ \ \ \ 0.8447\\$$

Construct and interpret a 99% confidence interval for the true concentration

$$\mu$$

.

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

An average human produces about 10 MJ of heat each day through metabolic activity. If a human body were an isolated system of mass 65 kg with the heat capacity of water, what temperature rise would the body experience? Human bodies are actually open systems, and the main mechanism of heat loss is through the evaporation of water. What mass of water should be evaporated each day to maintain constant temperature?

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.