# stats

## Project Description:

babe ruth, who played in the 1920’s and 1930’s, was the record-holding home-run hitter in professional baseball for many years. in the late 1990’s, mark mcgwire set a new record. following are the data for their season home runs. make back to back stemplots for the two data sets and then compare the distributions. who do you think was the better home-run hitter? explain your reasoning.
mcgwire 49 32 33 39 22 42 9 9 39 52 58 70 65 32 29
ruth 54 59 35 41 46 25 47 60 54 46 49 46 41 34 22

2. chocolate bars produced by a certain machine are labeled as 8.0 oz. the distribution of the actual weights of these chocolate bars is normal with a mean of 8.1 oz. and a standard deviation of 0.1 oz. a chocolate bar is considered underweight if it weighs less than 8.0 oz. (show your work for full credit).

a. the proportion of chocolate bars weighing less than 8.0 oz. is:

b. the proportion of chocolate bars with weights between 8.2 and 8.3 oz. is:

c. how should the chocolate bar wrappers be labeled so only 1% of bars produced are underweight?

3. statisticians prefer large samples. describe the effect of increasing the size of a sample on each of the following: (show your work for full credit).

a) the margin of error of a 95% confidence interval.

b) the p-value of a test, when ho is false and all facts about the population remain unchanged as n increases.

4. the mean score of adult men on a psychological test that measures “masculine stereotypes” is 4.88. a researcher studying hotel managers suspects that successful managers score higher than adult men in general. a random sample of 48 managers of large hotels has mean x̄ = 5.11. (show your work for full credit).

a) the null hypothesis for the researcher’s test is:

b) the alternative hypothesis for the test is:

c) suppose that scores of hotel managers on the test are normal with standard deviation σ = 0.79. the value of the test statistic is:

d) find the p-value of the test statistic:

e) is the p-value statistically significant at α = .05?

f) is the p-value statistically significant at α = .01?

5. the level of nitrogen oxides (nox) in the exhaust of cars of a particular model varies normally with mean 0.2 grams per mile (g/mi) and standard deviation 0.05 g/mi. government regulations call for nox emissions no higher than 0.3 g/mi. (show your work for full credit).

a) what is the probability that a single car of this model fails to meet the nox requirement?

b) a company has 25 cars of this model in this fleet. what is the probability that the average nox level x̄ of these cars is above 0.3 g/mi limit?

6. here are measurements (in millimeters) of a critical dimension on a sample of automobile engine crankshafts.
224.017 224.902 223.961 223.980
224.001 223.889 223.982 224.098
224.089 223.987 223.976 223.989
224.057 223.913 223.999 223.880

data set available under tasks 6 december 2012 in bb
the manufacturing process is known to vary normally with standard deviation σ = 0.06 mm. the process mean is supposed to be 224 mm. do these data give evidence that the process mean is not equal to the target value 224 mm?
a. state the null hypothesis (ho) and alternative (ha) that you will test.

b. calculate the test statistic z.

c. (7 pts) give the p-value of the test. are you convinced that the process mean in not 224 mm? why or why not.

d. (3 pts) at what level of α is this test statistically significant.

7. sue’s parents are concerned that she seems short for her age. their doctor has the following record of sarah’s height: (show your work for full credit).

age (months) 36 48 51 54 57 60
height (cm) 86 90 91 93 94 95

a. make a scatterplot of these data.

b. what is the least-squares regression line of height on age? plot this line on your scatterplot by predicting sue’s height at 40 and 60 months. are these heights good predictions or not. explain how you know if they are or are not.

c. what is sue’s rate of growth? if girls in the predicted age range grow normally at 6 cm gain, is sue on track for normal growth or not? explain your reasoning,

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