1 )A random sample of 46 adult coyotes in a region of northern Minnesota showed the average age to be x = 2.05 years, with sample standard deviation s = 0.84 years. However, it is thought that the overall population mean age of coyotes is = 1.75. Do the sample data indicate that coyotes in this region of northern Minnesota tend to live longer than the average of 1.75 years? Use = 0.01.

(a) What is the level of significance?

State the null and alternate hypotheses.

H0: = 1.75 yr; H1: > 1.75 yr

H0: > 1.75 yr; H1: = 1.75 yr

H0: = 1.75 yr; H1: 1.75 yr

H0: < 1.75 yr; H1: = 1.75 yr

H0: = 1.75 yr; H1: < 1.75 yr

(b) What sampling distribution will you use? Explain the rationale for your choice of sampling distribution.

The Student's t, since the sample size is large and is unknown.

The standard normal, since the sample size is large and is unknown.

The Student's t, since the sample size is large and is known.

The standard normal, since the sample size is large and is known.

What is the value of the sample test statistic? (Round your answer to three decimal places.)

(c) Find the P-value. (Round your answer to four decimal places.)

(d) Based on your answers in parts (a) to (c), will you reject or fail to reject the null hypothesis? Are the data statistically significant at level ?

At the = 0.01 level, we reject the null hypothesis and conclude the data are statistically significant.

At the = 0.01 level, we reject the null hypothesis and conclude the data are not statistically significant.

At the = 0.01 level, we fail to reject the null hypothesis and conclude the data are statistically significant.

At the = 0.01 level, we fail to reject the null hypothesis and conclude the data are not statistically significant.

(e) Interpret your conclusion in the context of the application.

There is sufficient evidence at the 0.01 level to conclude that coyotes in the specified region tend to live longer than 1.75 years.

There is insufficient evidence at the 0.01 level to conclude that coyotes in the specified region tend to live longer than 1.75 years.

2) Bill Alther is a zoologist who studies Anna's hummingbird (Calypte anna). Suppose that in a remote part of the Grand Canyon, a random sample of six of these birds was caught, weighed, and released. The weights (in grams) were as follows.

3.7 2.9 3.8 4.2 4.8 3.1

The sample mean is x = 3.75 grams. Let x be a random variable representing weights of hummingbirds in this part of the Grand Canyon. We assume that x has a normal distribution and = 0.60 gram. Suppose it is known that for the population of all Anna's hummingbirds, the mean weight is = 4.40 grams. Do the data indicate that the mean weight of these birds in this part of the Grand Canyon is less than 4.40 grams? Use = 0.01.

(a) What is the level of significance?

State the null and alternate hypotheses. Will you use a left-tailed, right-tailed, or two-tailed test?

H0: = 4.4 g; H1: < 4.4 g; left-tailed

H0: = 4.4 g; H1: > 4.4 g; right-tailed

H0: < 4.4 g; H1: = 4.4 g; left-tailed

H0: = 4.4 g; H1: 4.4 g; two-tailed

(b) What sampling distribution will you use? Explain the rationale for your choice of sampling distribution.

The Student's t, since we assume that x has a normal distribution with known .

The standard normal, since we assume that x has a normal distribution with unknown .

The Student's t, since n is large with unknown .

The standard normal, since we assume that x has a normal distribution with known .

What is the value of the sample test statistic? (Round your answer to two decimal places.)

(c) Find (or estimate) the P-value. (Round your answer to four decimal places.)

(d) Based on your answers in parts (a) to (c), will you reject or fail to reject the null hypothesis? Are the data statistically significant at level ?

At the = 0.01 level, we reject the null hypothesis and conclude the data are statistically significant.

At the = 0.01 level, we reject the null hypothesis and conclude the data are not statistically significant.

At the = 0.01 level, we fail to reject the null hypothesis and conclude the data are statistically significant.

At the = 0.01 level, we fail to reject the null hypothesis and conclude the data are not statistically significant.

(e) State your conclusion in the context of the application.

There is sufficient evidence at the 0.01 level to conclude that humming birds in the Grand Canyon weigh less than 4.40 grams.

There is insufficient evidence at the 0.01 level to conclude that humming birds in the Grand Canyon weigh less than 4.40 grams.

3) The method of tree ring dating gave the following years A.D. for an archaeological excavation site. Assume that the population of x values has an approximately normal distribution.

1215 1187 1201 1292 1268 1316 1275 1317 1275

(a) Use a calculator with mean and standard deviation keys to find the sample mean year x and sample standard deviation s. (Round your answers to the nearest whole number.)

x = A.D.

s = yr

(b) Find a 90% confidence interval for the mean of all tree ring dates from this archaeological site. (Round your answers to the nearest whole number.)

lower limit A.D.

upper limit A.D.

4) Suppose the heights of 18-year-old men are approximately normally distributed, with mean 67 inches and standard deviation 1 inches.

(a) What is the probability that an 18-year-old man selected at random is between 66 and 68 inches tall? (Round your answer to four decimal places.)

(b) If a random sample of eleven 18-year-old men is selected, what is the probability that the mean height x is between 66 and 68 inches? (Round your answer to four decimal places.)

(c) Compare your answers to parts (a) and (b). Is the probability in part (b) much higher? Why would you expect this?

The probability in part (b) is much lower because the standard deviation is smaller for the x distribution.

The probability in part (b) is much higher because the mean is smaller for the x distribution.

The probability in part (b) is much higher because the mean is larger for the x distribution.

The probability in part (b) is much higher because the standard deviation is larger for the x distribution.

The probability in part (b) is much higher because the standard deviation is smaller for the x distribution.

5) At Burnt Mesa Pueblo, archaeological studies have used the method of tree-ring dating in an effort to determine when prehistoric people lived in the pueblo. Wood from several excavations gave a mean of (year) 1238 with a standard deviation of 26 years. The distribution of dates was more or less mound-shaped and symmetrical about the mean. Use the empirical rule to estimate the following.

(a) a range of years centered about the mean in which about 68% of the data (tree-ring dates) will be found

between and A.D.

(b) a range of years centered about the mean in which about 95% of the data (tree-ring dates) will be found

between and A.D.

(c) a range of years centered about the mean in which almost all the data (tree-ring dates) will be found

between and A.D.