There Are 6 Questions on This Test Adding up to a Total of 105 Points. Read All the Questions

STP 420 Test 3

NAME:______ASU ID: ______

STP 420 SUMMER 2001

Exam 3

There are 6 questions on this test adding up to a total of 105 points. Read all the questions carefully.

Honor Policy: By signing below you confirm that you have neither given nor received any unauthorized assistance on this exam.

Signature: ______

Date: ______

Directions: Please read the questions carefully and place your answer in the space

provided at the end of each question. Show all necessary working.

1.[7] Ray is a basketball player who has missed about 30% of his free throws over several years. In a tournament game he missed 4 of 6 free throws. His coach says this was just bad luck. Suppose that Ray’s free throws are independent trials with probability 0.3 of a success (miss) on each trial. What is the probability that he misses 4 or more in the 6 free throw attempts? Use the binomial tables or the binomial formula.

2. The distribution of scores for persons over 16 years of age on the Wechsler Adult Intelligence Scale (WAIS) is approximately normal with mean 100 and standard deviation 15. The WAIS is one of the most common “IQ tests” for adults.

a.[5] What is the probability that a randomly chosen individual has a WAIS score of 105 or higher?

b.[8] What are the mean and standard deviation of the average WAIS score for an SRS of 60 people?

c.[5] What is the probability that the average WAIS score of an SRS of 60 people is 105 or higher?

d.[5] What is the exact distribution of for an SRS of 60 in part b above?

3. Patients with a chronic kidney failure may be treated by dialysis, using a machine that removes toxic wastes from the blood, a function normally performed by the kidneys. Kidney failure and dialysis can cause other changes, such as retention of phosphorus that must be corrected by changes in diet. A study of the nutrition of dialysis patients measured the level of phosphorus in the blood of several patients on six occasions. Here are the data for one patient (in milligrams of phosphorus per deciliter of blood)

5.6 5.1 4.6 4.8 5.7 6.4

The measurements are separated in time and can be considered an SRS of the patient’s blood phosphorus level. Assuming that this level varies normally with

s = 0.9 mg/dl.

a.[5] Find the mean of the sample data.

b.[6] Find the standard deviation of the sample data.

c.[12] Compute a 90% confidence interval for the mean blood phosphorus level.

4.[15] An agronomist examines the cellulose content of a variety of alfalfa hay. Suppose that the cellulose content in the population has standard deviation s = 8 milligrams per gram (mg/g). A sample of 15 cuttings has mean cellulose content = 145 mg/g. The agronomist has previous information which suggest that the mean is higher than m = 140 mg/g. Carryout a significance test at the a = 0.05 significance level to determine if the agronomist is right in saying that the mean is higher than m. Please include all necessary steps and state your conclusion in words.

5. A manufacturer of small appliances employs a market research firm to estimate retail sales of its products by gathering information from a sample of retail stores. An SRS of 50 stores in the Midwest sales region were asked to give the number of the manufacturer’s electric can openers that were sold last month. Here are the data:

19 / 19 / 16 / 19 / 24 / 26 / 24 / 63 / 22 / 16
13 / 26 / 34 / 10 / 48 / 16 / 20 / 14 / 13 / 24
34 / 14 / 25 / 16 / 26 / 25 / 25 / 26 / 11 / 79
17 / 25 / 18 / 15 / 13 / 35 / 17 / 15 / 21 / 12
19 / 20 / 32 / 19 / 24 / 19 / 17 / 41 / 24 / 27

The sample mean = 23.54 and the sample standard deviation

s = 12.52.

a.[12] Construct a 95% confidence interval for the mean number of can openers sold by all stores in the region.

b.[15] Carryout a significance test at the a = 0.01 significance level to determine if the mean = 23.54 is higher than m = 20. Please include all necessary steps and state your conclusion is words.

6. Does cocaine used by pregnant women cause their babies to have low birth weight? To study this question, birth weights of babies of women who tested positive for cocaine/crack during a drug-screening test were compared with the birth weights for women who either tested negative or were not tested, a group were call “other”. Here are the summary statistics. The birth weights are measured in grams. (Data from a study conducted at the Medical University of South Carolina in 1989.)

Group / n / / s
Positive Test / 134 / 2733 / 599
Other / 5974 / 3118 / 672

a.[10] Construct a 95% confidence interval for the mean difference in birth weights.

FORMULAE

Standard deviation of X:

Binomial mean and mX = np

Binomial standard deviation

Mean of a sample proportion

Standard Deviation of a sample proportion

X is approximately N(np, )

is approximately N(p,)

Binomial probability is

Level C confidence interval for m is s - known

Sample size

Test statistic

Standard error

One sample t statistic

One-Sample t Confidence Interval s - unknown

Two-sample t statistic from t(k) for k smaller of n1-1 and n2-2

Confidence interval for m1 - m2 is given by

STP 420 TEST 3 SUMMER 2001