Question

1. Suppose a mutual fund qualifies as having moderate risk if the standard deviation of its monthly rate of return is less than 6​%. A​ mutual-fund rating agency randomly selects 24 months and determines the rate of return for a certain fund. The standard deviation of the rate of return is computed to be 4.14​%. Is there sufficient evidence to conclude that the fund has moderate risk at the a=0.10 level of​ significance? A normal probability plot indicates that the monthly rates of return are normally distributed.

a.

What are the correct hypotheses for this​ test?

The null hypothesis is H0​: (o,μ,p) (<,>,=, ≠) BLANK

The alternative hypothesis is H1​: (o,μ,p) (<,>,=, ≠) BLANK

b. Calculate the value of the test statistic.

c. Use technology to determine the​ P-value for the test statistic.

The​ P-value is=

d. What is the correct conclusion at the a=0.10 level of​ significance?

Since the​ P-value is (greater, less) than the level of​ significance, (do not reject, reject) the null hypothesis. There (is not, is) sufficient evidence to conclude that the fund has moderate risk at the 0.10 level of significance.

2. A graduate student conducted an experiment in which 18 ​ten-month-old babies were asked to watch a climber character attempt to ascend a hill. On two​ occasions, the baby witnesses the character fail to make the climb. On the third​ attempt, the baby witnesses either a helper toy push the character up the hill or a hinderer toy prevent the character from making the ascent. The helper and hinderer toys were shown to each baby in a random fashion for a fixed amount of time. The baby was then placed in front of each toy and allowed to choose which toy he or she wished to play with. In 15 of the 18 ​cases, the baby chose the helper toy. Complete parts ​(a) through ​(d) below.

a. Why is it important to randomly expose the baby to the helper or hinderer toy​ first?

A. The randomness in the order of exposure is important to avoid bias.

B.The randomness in the order of exposure is important to minimize the effect of the sample standard deviation.

C.The randomness in the order of exposure is important to make sure half the babies see the helper first and the other half see the hinderer first.

D. The randomness in the order of exposure is important to satisfy the conditions of using the binomial probability distribution.

b. What would be the appropriate null and alternative hypotheses if the researcher is attempting to show that babies prefer helpers over​ hinderers?

H0:p (<,>,=, ≠) 0.5

H1:p (<,>,=, ≠) 0.5

c. Use the binomial probability formula to determine the​ P-value for this test.

​P-value=

What is the correct conclusion regarding the null​ hypothesis?

A. Do not reject H0.Although no level of significance is​ given, there is sufficient evidence to suggest the proportion of babies who choose the helper toy is greater than 0.5.

B. Reject H0.Although no level of significance is​ given, there is sufficient evidence to suggest the proportion of babies who choose the helper toy is greater than 0.5.

C. Reject H0. Although no level of significance is​ given, there is insufficient evidence to suggest the proportion of babies who choose the helper toy is greater than 0.5.

D. Do not reject H0.Although no level of significance is​ given, there is insufficient evidence to suggest the proportion of babies who choose the helper toy is greater than 0.5.

d. In testing 12 ​six-month-old babies, all 12 preferred the helper toy. The​ P-value was reported as 0.0002. Interpret this result. Choose the correct answer below.

A. If the population proportion of babies who choose the helper is​ 0.5, a sample where all 12 babies choose the helper will occur in about 12 out of 1000 samples of 12 babies.

B. If the population proportion of babies who choose the helper is​ 0.5, a sample where all 12 babies choose the helper will occur in exactly 2 out of​ 10,000 samples of 12 babies.

C. If the population proportion of babies who choose the helper is​ 0.5, a sample where all 12 babies choose the helper will occur in exactly 12 out of 1000 samples of 12 babies.

D. If the population proportion of babies who choose the helper is​ 0.5, a sample where all 12 babies choose the helper will occur in about 2 out of​ 10,000 samples of 12 babies.

Answer 1