### 90% confidence interval for the difference between the mean summer earnings of male and female

Question 1Â

College financial aid offices expect students to use summer earnings to help pay for college. But how large are these earnings? One college studied this question by asking a sample of students how much they earned. Omitting students who were not employed, 1296 responses were received. Here are the data in summary form:

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Group n x s

Males 675 $3297.91 $2394.65

Females 621 $2380.68 $1815.55

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(a) Use the two-sample t procedures to give a 90% confidence interval for the difference between the mean summer earnings of male and female students.

(b) The distribution of earnings is strongly skewed to the right. Nevertheless, use of t procedures is justified. Why?

(c) Once the sample size was decided, the sample was chosen by taking every kth name from an alphabetical list of undergraduates. Is it reasonable to consider the sample as two SRSs chosen from the male and female undergraduate populations?

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Question 2Â

The pesticide DDT causes tremors and convulsions if it is ingested by humans or other mammals. Researchers seek to understand how the convulsions are caused. In a randomized comparative experiment, 6 white rats poisoned with DDT were compared with a control group of 6 un-poisoned rats. Electrical measurements of nerve activity are the main clue to the nature of DDT poisoning. When a nerve is stimulated, its electrical response shows a sharp spike followed by a much smaller second spike. Researchers found that the second spike is larger in rats fed DDT than in normal rats. This observation helps biologists understand how DDT causes tremors. The researchers measured the amplitude of the second spike as a percentage of the first spike when a nerve in the rat's leg was stimulated.

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Poisoned rats 12.207 16.869 25.0505 22.429 8.456 20.589

Unpoisoned rats 11.074 9.686 12.064 9.351 8.182 6.642

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Normal probability plots show no evidence of outliers or strong skewness. Both populations are reasonably normal, as far as can be judged from 6 observations. The difference in means is quite large, but in such small samples the sample mean is highly variable. A significance test can help confirm that we are seeing a real effect. Because the researchers did not conjecture in advance that the size of the second spike would increase in rats fed DDT, we testÂ

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H0: u1 = u2

H1: u1<u2

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Carry out the complete significance test.

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Question 3Â

A bank compares two proposals to increase the amount that its credit card customers charge on their cards. (The bank earns a percentage of the amount charged, paid by the stores that accept the card.) Proposal A offers to eliminate the annual fee for customers who charge $2400 or more during the year. Proposal B offers a small percent of the total amount charged as a cash rebate at the end of the year. The bank offers each proposal to an SRS of 150 of its existing credit card customers. At the end of the year, the total amount charged by each customer is recorded. Here are the summary statistics:

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Group n x s

A 150 $1987 $392

B 150 $2056 $413

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a) Do the data show a significant difference between the mean amounts charged by customers offered the two plans? Carry out a complete test.

b) The distributions of amounts charged are skewed to the right, but outliers are prevented by the limits that the bank imposes on credit balances. Do you think that skewness threatens the validity of the test? Explain your answer.

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Question 4Â

Below is the formula we used to find the test statistic t for a single sample. Copy and paste the formula into the answer box and adjust it to find the test statistic t for the 2-sample interval.

t= xbar-U /s /squareroot of n

# Answers

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