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 credit card customers. At the end of the year, the total amount charged by each customer is recorded. Here are the summary statistics:

Group	n	$ $\bar{x}	s
A	150	$1987	$392
B	150	$2056	$413

Is the bank's study an experiment? Why? How does this affect the conclusions the bank can draw from the study?

A market research firm supplies manufacturers with estimates of the retail sales of their products from samples of retail stores. Marketing managers are prone to look at the estimate and ignore sampling error. An SRS of 75 stores this month shows mean sales of 52 units of a small appliance, with standard deviation 13 units. During the same month Last year, an SRS of 53 stores gave mean sales of 49 units, with standard deviation 11 units. An increase from 49 to 52 is a rise of 6%. The marketing manager is happy, because sales are up 6%.

Use the two-sample t procedure to give a 95% confidence interval for the difference between this year and last year in the mean number of units sold at all retail stores.

Physical fitness is related to personality characteristics. In one study of this relationship, middle-aged college faculty who had volunteered for a fitness program were divided into low-fitness and high-fitness groups based on a physical examination. The subjects then took the Cattell Sixteen Personality Factor Questionnaire. Here are the data for the "ego strength" personality factor:

You should be hesitant to generalize these results to the population of all middle-aged men. Explain why.

Physical fitness is related to personality characteristics. In one study of this relationship, middle-aged college faculty who had volunteered for a fitness program were divided into low-fitness and high-fitness groups based on a physical examination. The subjects then took the Cattell Sixteen Personality Factor Questionnaire. Here are the data for the "ego strength" personality factor:

Is the difference in mean ego strength significant at the 5% level? At the 1% level? Be sure to state $H_0$ and $H_a$.

A study of iroa deficiency in infants compared samples of infants whooe mothers chose different ways of feeding them. One group contained breastfed infank. The children in another group were fed a standard baby formula without any iron supplements. Here are summary results on blaod hemoglobin levels at 12 months of age:

Is this study an experiment? Why? How does this affect the conclur sions we can draw from the study?

A study of iroa deficiency in infants compared samples of infants whooe mothers chose different ways of feeding them. One group contained breastfed infank. The children in another group were fed a standard baby formula without any iron supplements. Here are summary results on blaod hemoglobin levels at 12 months of age:

State the assamptions that your procedures in (a) and (b) require in order to be valid.

A study of iroa deficiency in infants compared samples of infants whooe mothers chose different ways of feeding them. One group contained breastfed infank. The children in another group were fed a standard baby formula without any iron supplements. Here are summary results on blaod hemoglobin levels at 12 months of age:

Give a 95% confidence interval for the mean difference in hemoglobin level between the two populations of infants.

A study of iroa deficiency in infants compared samples of infants whooe mothers chose different ways of feeding them. One group contained breastfed infank. The children in another group were fed a standard baby formula without any iron supplements. Here are summary results on blaod hemoglobin levels at 12 months of age:

Is there significant evidence that the mean hemoglobin level is different among, breast-fed babes? State $H_0$ and $H_a$ and carry out a t test. Give the P-value. What is your conclusion?

The Johns Hopkins Regional Talent Searches give the Scholastic Assessment Tests (intended for high school juniors and seniors) to 1 3-year-olds. In all, 19,563 males and 19,937 females took the tests between 1980 and 1982. The mean scores of males and females on the verbal test are nearly equal, but there is a clear difference between the sexes on the mathematics test. The reason for this difference is not understood. Here are the data:

Give a 99% confidence interval for the difference between the mean score for males and the mean score for females in the population that Johns Hopkins searches. Must S.AT scores have a normal distribution in order. for your confidence interval to be valid? Why?

What aspects of rowing technique distinguish between novice and skilled competitive rowers? Researchers compared two groups of female competitive rowers: a group of skilled rowers and a group of novices. The researchers measured many mechanical aspects of the rowing style as the subjects rowed on a Stanford Rowing Ergometer. One important variable is the angular velocity of the knee, which describes the rate at which the knee joint opens as the legs push the body back on the sliding seat. The data show no outliers or strong skewness. Here is the SAS computer output:

TEST PROCEDURE Variable: KNEE

Give a 90% confidence interval for the mean difference between the knee velocities of skilled and novice female rowers.

What aspects of rowing technique distinguish between novice and skilled competitive rowers? Researchers compared two groups of female competitive rowers: a group of skilled rowers and a group of novices. The researchers measured many mechanical aspects of the rowing style as the subjects rowed on a Stanford Rowing Ergometer. One important variable is the angular velocity of the knee, which describes the rate at which the knee joint opens as the legs push the body back on the sliding seat. The data show no outliers or strong skewness. Here is the SAS computer output:

TEST PROCEDURE Variable: KNEE

What is the value of the two-sample t statistic and its P-value? (Note that SAS provides two-sided P-values. If you need a one-sided P-value, divide the two-sided value by 2) What do you conclude?

What aspects of rowing technique distinguish between novice and skilled competitive rowers? Researchers compared two groups of female competitive rowers: a group of skilled rowers and a group of novices. The researchers measured many mechanical aspects of the rowing style as the subjects rowed on a Stanford Rowing Ergometer. One important variable is the angular velocity of the knee, which describes the rate at which the knee joint opens as the legs push the body back on the sliding seat. The data show no outliers or strong skewness. Here is the SAS computer output:

TEST PROCEDURE Variable: KNEE

The researchers believed that the knee velocity would be higher for skilled rowers. State $H_0$ and $H_a$.

The mentioned example reports the analysis of data on the effects of DDT poisoning. The software uses the two-sample t-test with degrees of freedom given in the box. Starting from the computer's results for $\bar{x}_i$ and $s_i$, verify the computer's values for the test statistic t=2.99 and the degrees of freedom $\mathrm{df}$=5.9.

Use your TI-83/89 and the two-sample procedures to replicate the results of the DDT-nerve stimulus experiment in the mentioned example. Verify that you get the same t-test statistic and P-value.