1. Letxbe a random variable representing dividend yield of bank stocks. We may assume thatxhas a normal distribution with=2.7%.A random sample of10 bankstocks gave the following yields (in percents).

• 5.7 4.8 6.0 4.9 4.0 3.4 6.5 7.1 5.3 6.1

The sample mean is= 5.38%. Suppose that for the entire stock market, the mean dividend yield is=4.6%.Do these data indicate that the dividend yield of all bank stocks is higher than4.6%? Use=0.01.

(a) What is the level of significance? (Enter a number.) State the null and alternate hypotheses. Will you use a left-tailed, right-tailed, or two-tailed test? i. H₀:= 4.6%;H₁:<4.6%; left-tailed

ii. H₀:= 4.6%;H₁:4.6%; two-tailed

iii. H₀:>4.6%;H₁:= 4.6%; right-tailed

iv. H₀:= 4.6%;H₁:>4.6%; right-tailed

(b) What sampling distribution will you use? Explain the rationale for your choice of sampling distribution. i. The standard normal, since we assume thatxhas a normal distribution with unknown.

ii. The Student'st, since we assume thatxhas a normal distribution with known.

iii. The Student'st, sincenis large with unknown.

iv. The standard normal, since we assume thatxhas a normal distribution with known.

Compute thezvalue of the sample test statistic. (Enter a number. Round your answer to two decimal places.) (c) Find (or estimate) theP-value. (Enter a number. Round your answer to four decimal places.)

2. Bill Alther is a zoologist who studies Anna's hummingbird (Calypte anna). (Reference: Hummingbirds, K. Long, W. Alther.) 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= 3.75 grams. Letxbe a random variable representing weights of hummingbirds in this part of the Grand Canyon. We assume thatxhas a normal distribution and=0.64gram.Suppose it is known that for the population of all Anna's hummingbirds, the mean weight is=4.30grams.Do the data indicate that the mean weight of these birds in this part of the Grand Canyon is less than4.30grams?Use=0.10.

(a) What is the level of significance? (Enter a number.) State the null and alternate hypotheses. Will you use a left-tailed, right-tailed, or two-tailed test? i. H₀:< 4.3 g;H₁:= 4.3 g; left-tailed

ii. H₀:= 4.3 g;H₁:< 4.3 g; left-tailed

iii. H₀:= 4.3 g;H₁:> 4.3 g; right-tailed

iv. H₀:= 4.3 g;H₁:4.3 g; two-tailed

(b) What sampling distribution will you use? Explain the rationale for your choice of sampling distribution. i. The standard normal, since we assume thatxhas a normal distribution with known.

ii. The Student'st, since we assume thatxhas a normal distribution with known.

iii. The Student'st, sincenis large with unknown.

iv. The standard normal, since we assume thatxhas a normal distribution with unknown.

Compute thezvalue of the sample test statistic. (Enter a number. Round your answer to two decimal places.) (c) Find (or estimate) theP-value. (Enter a number. Round your answer to four decimal places.)