On an ostrich farm, the weights of the birds are found to be normally distributed. The weights of the females have a mean 78.6 kg and a standard deviation of 5.03 kg. The weights of the males have a mean 91.3 kg and a standard deviation of 6.29 kg. Find the probability that a randomly selected: Male will weight less than 80 kg. Female will weight less than 80 kg. Female will weigh between 70 and 80 kg. 20% of females weigh less than k kg. Find k. The middle 90% of the males weigh between a kg and b kg. Find the values of a and b kg.

The following data come from a study designed to investigate drinking problems among college students. In 1983, a group of students were asked whether they had ever driven an automobile while drinking. In 1987, after the legal drinking age was raised, a different group of college students were asked the same question. SHOW EXCEL CODES

Drove While Drinking Year

1983 1987 Total

Yes 1250 991 2241

No 1387 1666 3053

Total 2637 2657 5294

A. Use the chi-square test to evaluate the null hypothesis that population proportions of students who drove while drinking are the same in the two calendar years.

B. What do you conclude about the behavior of college students?

C. Again test the null hypothesis that the proportions of students who drove while drinking are identical for the two calendar years. This time, use the method based on the normal approximation to the binomial distribution that was presenting in Section 14.6. Do you reach the same conclusion?

D. Construct a 95% confidence interval for the true difference in population proportions.

E. Does the 95% confidence interval contain the value 0? Would you have expected it to?

Since an instant replay system for tennis was introduced at a major​ tournament, men challenged

14371437

referee​ calls, with the result that

431431

of the calls were overturned. Women challenged

745745

referee​ calls, and

227227

of the calls were overturned. Use a

0.010.01

significance level to test the claim that men and women have equal success in challenging calls. Complete parts​ (a) through​ (c) below.

a. Test the claim using a hypothesis test.

Consider the first sample to be the sample of male tennis players who challenged referee calls and the second sample to be the sample of female tennis players who challenged referee calls. What are the null and alternative hypotheses for the hypothesis​ test?

A.

Upper H 0H0​:

p 1p1not equals≠p 2p2

Upper H 1H1​:

p 1p1equals=p 2p2

B.

Upper H 0H0​:

p 1p1equals=p 2p2

Upper H 1H1​:

p 1p1greater than>p 2p2

C.

Upper H 0H0​:

p 1p1less than or equals≤p 2p2

Upper H 1H1​:

p 1p1not equals≠p 2p2

D.

Upper H 0H0​:

p 1p1equals=p 2p2

Upper H 1H1​:

p 1p1less than<p 2p2

E.

Upper H 0H0​:

p 1p1equals=p 2p2

Upper H 1H1​:

p 1p1not equals≠p 2p2

F.

Upper H 0H0​:

p 1p1greater than or equals≥p 2p2

Upper H 1H1​:

p 1p1not equals≠p 2p2

Identify the test statistic.

zequals=negative . 23−.23

​(Round to two decimal places as​ needed.)

Identify the​ P-value.

​P-valueequals=. 818.818

​(Round to three decimal places as​ needed.)

What is the conclusion based on the hypothesis​ test?

The​ P-value is

greater than

the significance level of

alphaαequals=0.010.01​,

so

fail to reject

the null hypothesis. There

is not sufficient

evidence to warrant rejection of the claim that women and men have equal success in challenging calls.

b. Test the claim by constructing an appropriate confidence interval.

The

9999​%

confidence interval is

nothingless than<left parenthesis p 1 minus p 2 right parenthesisp1−p2less than<nothing.

​(Round to three decimal places as​ needed.)

What is the conclusion based on the confidence​ interval?

Because the confidence interval limits

▼

do not include

include

​0, there

▼

does

does not

appear to be a significant difference between the two proportions. There

▼

is not sufficient

is sufficient

evidence to warrant rejection of the claim that men and women have equal success in challenging calls.

c. Based on the​ results, does it appear that men and women may have equal success in challenging​ calls?

A.

The confidence interval suggests that there is a significant difference between the success of men and women in challenging calls. It is reasonable to speculate that women have more success.

B.

The confidence interval suggests that there is no significant difference between the success of men and women in challenging calls.

C.

The confidence interval suggests that there is a significant difference between the success of men and women in challenging calls. It is reasonable to speculate that men have more success.

D.

There is not enough information to reach a conclusion.

A bus travels between two cities A and B that are 100 miles apart.Two service stations are located at mile 30 and mile 70, as well as in the cities themselves. The bus breaks down on the road. Assuming the place of breakdown is uniformly distributed between the cities, what is the probability that it is no more than 10 miles to the nearest service station? What is the expectation of the distance to the nearest service station?

The researchers classified gas turbines into three categories: traditional, advanced, and aeroderivative. Mean heat rate and standard deviation of heat rate for

• Advanced are 9764 and 639
• Aeroderiv are 12312 and 2652
• Traditional are 11544 and 1279

Is there sufficient evidence of a difference between the mean heat rates of traditional turbines and aeroderivative turbines at  alpha =0.05 ? Show all the work

Briefly describe the product-process matrix and the customer-contact matrix for service processes。

In a clinical trial, 401,974 adults were randomly assigned to two groups. The treatment group consisted of 201,229 adults given a vaccine and the other 200,745 adults were given a placebo. Among the adults in the treatment group, 33 adults developed the disease and among the placebo group, 115 adults developed the disease. The doctors' claim that the rate for the group receiving the vaccine is less than the group receiving the placebo. Answer the following questions:

a. If w idenitfy the symbolic null and alternative hypothesis.

b. If the P-value for this test is reported as "less than 0.001", what is your decision? What would you conclude about the original claim?

c. Assume that we want to use a 0.05 significance level to test the claim that p1 < p2. If we want to test that claim by using a confidence interval, what confidence level should we use?

d. If we test the original claim, we get the confidence interval -0.000508 < p1 - p2 < −0.000309 , what does this confidence interval suggest about the claim? e. In general, when dealing with inferences for two population proportions, which two of the following are equivalent: Confidence Interval method; P-value method; Critical Value method? Explain.

Jobs and productivity! How do retail stores rate? One way to answer this question is to examine annual profits per employee. The following data give annual profits per employee (in units of 1 thousand dollars per employee) for companies in retail sales. Assume σ ≈ 3.7 thousand dollars.

(a) Use a calculator or appropriate computer software to find x for the preceding data. (Round your answer to two decimal places.)
thousand dollars per employee

(b) Let us say that the preceding data are representative of the entire sector of retail sales companies. Find an 80% confidence interval for μ, the average annual profit per employee for retail sales. (Round your answers to two decimal places.)

c) Find an 95% confidence interval for μ, the average annual profit per employee for retail sales. (Round your answers to two decimal places.)

The following data represent petal lengths (in cm) for independent random samples of two species of Iris.

Petal length (in cm) of Iris virginica: x₁; n₁ = 35

Petal length (in cm) of Iris setosa: x₂; n₂ = 38

(a) Use a calculator with mean and standard deviation keys to calculate x₁, s₁, x₂, and s₂. (Round your answers to two decimal places.)

(b) Let μ₁ be the population mean for x₁ and let μ₂ be the population mean for x₂. Find a 99% confidence interval for μ₁ − μ₂. (Round your answers to two decimal places.)

David E. Brown is an expert in wildlife conservation. In his book The Wolf in the Southwest: The Making of an Endangered Species (University of Arizona Press), he records the following weights of adult grey wolves from two regions in Old Mexico.

Chihuahua region: x₁ variable in pounds

Durango region: x₂ variable in pounds

(a) Use a calculator with mean and standard deviation keys to calculate x₁, s₁, x₂, and s₂. (Use 2 decimal places.)

(b) Let μ₁ be the mean weight of the population of all grey wolves in the Chihuahua region. Let μ₂ be the mean weight of the population of all grey wolves in the Durango region. Find a 99% confidence interval for μ₁ – μ₂. (Use 2 decimal places.)

To evaluate the performance of inspectors in a new company, a quality manager had a sample of 12 novice inspectors evaluate 200 finished products. The same 200 items were evaluated by 12 experienced inspectors. SD of error for the novice inspectors was 8.64 and for the experiences inspectors was 5.74.

Was the variance in inspection errors lower for experienced inspectors than for novice inspectors? Conduct a hypothesis testing at  alpha = 0.05 and show all the work.

The number of men and women among professors in Math, Physics, Chemistry, Linguistics, and English departments from a SRS of small colleges were counted, and the results are shown in the table below.

Test the claim that the gender of a professor is independent of the department. Use the significance level α=0.01

(a) The test statistic is χ^2=

Suppose 130 geology students measure the mass of an ore sample. Due to human error and limitations in the reliability of the​ balance, not all the readings are equal. The results are found to closely approximate a normal​ curve, with mean

82g and standard deviation

1g. Use the symmetry of the normal curve and the empirical rule as needed to estimate the number of students reporting readings between 79

g and 85g.

The length of time to complete a door assembly on an automobile factory assembly line is normally distributed with mean μ=7.3 minutes and standard deviation σ=2 minutes. Samples of size 70 are taken. What is the mean value for the sampling distribution of the sample means?

The length of time to complete a door assembly on an automobile factory assembly line is normally distributed with mean μ=7.2 minutes and standard deviation σ=2.4 minutes. Samples of size 100 are taken. To the nearest thousandth of a minute, what is the standard deviation of the sampling distribution of the sample means?

Find P(46≤x¯≤53) for a random sample of size 35 with a mean of 51 and a standard deviation of 12.   (Round your answer to four decimal places.)

At a gymnastics meet, three judges evaluate the balance beam performances of five gymnasts. The judges use a scale of 1 to 10, where 10 is a perfect score. A statistician wants to examine the objectivity and consistency of the judges. Assume scores are normally distributed. (You may find it useful to reference the q table.)

a-1. Construct an ANOVA table. (Round intermediate calculations to at least 4 decimal places. Round "SS", "MS", "p-value" to 4 decimal places and "F" to 3 decimal places.)

a-2. If average scores differ by gymnast, use Tukey’s HSD method at the 5% significance level to determine which gymnasts’ performances differ. (Negative values should be indicated by a minus sign. Round intermediate calculations to at least 4 decimal places. Round your answers to 2 decimal places.)