For which of the following settings might it be reasonable to use a binomial distribution to describe the random variable X?

1.) 25 Pittsburgh residents were asked how much sleep they get per night. The mean was 7.2 hours and the standard deviation was 0.78 hours. Construct and interpret a 90% confidence interval for the true mean number of hours of sleep that Pittsburgh residents get per night.

2.) A sample of 11 Chevy Volt drivers resulted in them having a mean of 42.6 miles per gallon (mpg) and a standard deviation of 4.8 mpg. Construct and interpret a 95% confidence interval for the mean gas mileage of all Chevy Volt drivers.

3.) A researcher believes the mean price of regular gas in Pennsylvania has increased from last month's mean of $2.88. A sample of 50 gas stations yields a mean price of $2.98 and a standard deviation of $0.50. Conduct a hypothesis test at the 10% significance level.  Make sure to give the hypotheses, test statistic, p-value, decision, and a practical interpretation.

b) Explain the purposes of the t test and the F test in multiple regression.

d) When can we experience autocorrelation in our data and how do we determine whether there is a first-order correlation (Explain)?

As part of an air pollution study, visibility in air was measured in three months at two altitude level.

Question 11

Given that the data neither follow normal distribution nor have equal variance, what is the appropriate test to determine if visibility varied with different months and altitude.

Select one:

a. Kruskal-Wallis Test

b. Two independent sample t test

c. Two-way ANOVA

d. Scheirer-Ray-Hare Test

Question 12

What are the degree of freedom for the altitude, month and error (Within) respectively?

Select one:

a. 1, 2, 2

b. 1, 2, 24

c. 1, 2, 4

d. 2, 3, 5

e. 2, 3, 29

Question 13

What is the conclusion for the variable altitude?

Select one:

a. Air visibility is unequal between different heights (calculated statistics = 0.015, p-value < 0.001)

b. Air visibility is equal between different heights (calculated statistics = 0.001, p-value > 0.05)

c. Air visibility is unequal between different heights (calculated statistics = 0.004, p-value < 0.05)

d. Air visibility is equal between different heights (calculated statistics = 0.015, p-value > 0.05)

Question 14

What is the conclusion for the variable Month?

Select one:

a. Air visibility is unequal among different months (calculated statistics = 9.72, 0.001 < p-value < 0.01)

b. Air visibility is unequal among different months (calculated statistics = 9.72, p-value < 0.001)

c. Air visibility is unequal among different months (calculated statistics = 25.98, p-value < 0.001)

d. Air visibility is equal among different months (calculated statistics = 25.98, p-value > 0.05)

Question 15

What is the conclusion for the interaction effect between altitude and Month?

Select one:

a. Interaction effect exists between altitude and Month (calculated statistics = 0.75, p-value < 0.05)

b. Interaction effect exists between altitude and Month (calculated statistics = 0.75, p-value < 0.01)

c. No interaction effect between altitude and Month (calculated statistics = 0.28, 0.05 < p-value < 0.1)

d. No interaction effect between altitude and Month (calculated statistics = 0.28, 0.75 < p-value < 0.90)

A social researcher is interested in understanding the effect of college education on wages. The workers in one group have earned an associate’s degree while members of the other group hold at least a bachelor’s degree. He would like to run a hypothesis test with α = .10 to see if those with a bachelor’s degree have significantly higher hourly wages than those with an associate’s degree.

a. Calculate standard deviation of the comparison distribution

1. Calculate the t statistic (2 points total: 1 for work and 1 for result)

2. Considering the research question and the hypotheses, should the test be one-tailed or two-tailed? Why? (2 points total: 1 for each answer)

3. Determine the critical t value(s) for this hypothesis test based on the degree of freedom, from (d), and the preset alpha level. (1 point total)

4. Compare the calculated t statistic with the critical t value by stating which is more “extreme”, and then make a decision about the hypothesis test by stating clearly “reject” or “fail to reject” the null hypothesis. (1 point total: .5 for comparison, .5 for decision)

e. Calculate the pooled standard deviation for the populations and then use it to calculate the standardized effect size of this test.

The school district recently adopted the use of e-textbooks, and the superintendent is interested in determining the level of satisfaction with e-textbooks among students and if there is a relationship between the level of satisfaction and student classification. The superintendent selected a sample of students from one high school and asked them how satisfied they were with the use of e-textbooks. The data that were collected are presented in the following table.

Table 1: Student Classification (N=128)

Questions

1. Of the students that were satisfied, what percent were Freshmen, Sophomore, Junior, and Senior? (Round your final answer to 1 decimal place).

2. State an appropriate null hypothesis for this analysis.

3. What is the value of the chi-square statistic?

4. What are the reported degrees of freedom?

5. What is the reported level of significance?

6. Based on the results of the chi-square test of independence, is there an association between e-textbook satisfaction and academic classification?

7. Present the results as they might appear in an article.

This must include a table and narrative statement that reports and interprets the results of the analysis. Note: The table must be created using your word processing program. Tables that are copied and pasted from SPSS are not acceptable.

An engineer designed a valve that will regulate water pressure on an automobile engine. The engineer designed the valve such that it would produce a mean pressure of 4.3 pounds/square inch. It is believed that the valve performs above the specifications. The valve was tested on 12 engines and the mean pressure was 4.7 pounds/square inch with a standard deviation of 0.9. A level of significance of 0.05 will be used. Assume the population distribution is approximately normal. Determine the decision rule for rejecting the null hypothesis. Round your answer to three decimal places. Reject H0 if t >

The data are daily high temperatures in Atlanta for one month.

61, 61, 63, 64, 65, 66, 66, 66, 67, 68, 70, 70, 70, 71, 71, 72, 74, 74, 74, 75, 75, 75, 76, 76, 77, 78, 78, 79, 79, 94

Question 1 options:

Question 2:

The height in feet of 25 trees is shown below (lowest to highest).

21, 27, 30, 31, 31, 31, 33, 34, 34, 37, 38, 38, 38, 40, 41, 42, 43, 45, 46, 51, 51, 52, 52, 59, 59

Question 2 options:

Let x be a random variable that represents white blood cell count per cubic milliliter of whole blood. Assume that x has a distribution that is approximately normal, with mean μ = 6150and estimated standard deviation σ = 2200. A test result of x < 3500 is an indication of leukopenia. This indicates bone marrow depression that may be the result of a viral infection.

(a) What is the probability that, on a single test, x is less than 3500? (Round your answer to four decimal places.)


(b) Suppose a doctor uses the average x for two tests taken about a week apart. What can we say about the probability distribution of x?

The probability distribution of x is not normal.The probability distribution of x is approximately normal with μ_x = 6150 and σ_x = 1555.63.     The probability distribution of x is approximately normal with μ_x = 6150 and σ_x = 2200.The probability distribution of x is approximately normal with μ_x = 6150 and σ_x = 1100.00.

What is the probability of x < 3500? (Round your answer to four decimal places.)


(c) Repeat part (b) for n = 3 tests taken a week apart. (Round your answer to four decimal places.)


(d) Compare your answers to parts (a), (b), and (c). How did the probabilities change as n increased?

The probabilities decreased as n increased.The probabilities increased as n increased.     The probabilities stayed the same as n increased.

If a person had x < 3500 based on three tests, what conclusion would you draw as a doctor or a nurse?

It would be an extremely rare event for a person to have two or three tests below 3,500 purely by chance. The person probably has leukopenia.It would be a common event for a person to have two or three tests below 3,500 purely by chance. The person probably does not have leukopenia.     It would be a common event for a person to have two or three tests below 3,500 purely by chance. The person probably has leukopenia.It would be an extremely rare event for a person to have two or three tests below 3,500 purely by chance. The person probably does not have leukopenia.

Here is a data set ( n = 117 )

that has been sorted.

14.2 21.3 22.5 22.9 23.3 23.8 23.9 24.8 25.1 26.6 26.9 26.9 27.3 27.4 27.5 27.8 28.2 28.3 28.5 28.6 28.6 29.1 29.6 29.7 29.7 29.9 30.2 30.5 30.6 30.6 30.9 31.2 31.4 31.7 31.8 31.8 32 32 32.2 32.3 32.3 32.3 32.6 32.9 33.4 33.7 33.9 33.9 34.2 34.4 34.8 34.9 34.9 35.1 35.3 35.6 35.7 36 36.4 36.7 36.8 36.9 37 37 37.1 37.1 37.2 37.3 37.4 37.6 37.7 38 38.1 38.7 39.2 39.3 39.4 39.5 39.6 39.6 40.2 40.5 40.5 40.6 41.3 41.5 41.7 42.3 42.3 43.3 43.4 43.4 43.5 43.5 43.8 43.9 44.4 44.5 44.6 44.9 45.1 45.9 46 46.5 46.9 47.2 47.3 47.6 48.2 49 49.3 49.4 49.6 50.4 51.3 51.6 53.3

To find P55, what is the value of the locator? L =

Use the locator, give the value for the 55-Percentile: P55 =

Coal is carried from a mine in West Virginia to a power plant in New York in hopper cars on a long train. The automatic hopper car loader is set to put 60 tons of coal into each car. The actual weights of coal loaded into each car are normally distributed, with mean μ = 60 tons and standard deviation σ = 1.6 ton.

(a) What is the probability that one car chosen at random will have less than 59.5 tons of coal? (Round your answer to four decimal places.)


(b) What is the probability that 50 cars chosen at random will have a mean load weight x of less than 59.5 tons of coal? (Round your answer to four decimal places.)


(c) Suppose the weight of coal in one car was less than 59.5 tons. Would that fact make you suspect that the loader had slipped out of adjustment?

Yes or No     

Suppose the weight of coal in 50 cars selected at random had an average x of less than 59.5 tons. Would that fact make you suspect that the loader had slipped out of adjustment? Why?

Yes, the probability that this deviation is random is very small.Yes, the probability that this deviation is random is very large.     No, the probability that this deviation is random is very small.No, the probability that this deviation is random is very large.

Find the critical value of t given the following.

1. t_0.05 for a t-distribution with 34 degrees of freedom
   1. 1.691                            b.   2.728                      c.   2.032                       d.   2.441

Use the confidence level and sample data to find the margin of error E.

2. Weights of eggs: 90% confidence;  n = 40,  = 1.54 oz.,  s = 0.41 oz.
   1. 0.107 oz.                      b.   0.109 oz.                 c.   0.112 oz.                 d.   0.030 oz.

Use the confidence level and sample data to find a confidence interval for estimating the population μ.

3. Weights of eggs: 90% confidence;  n = 40,  = 1.54 oz.,  s = 0.41 oz.
   1. 1.433 < μ <  1.647         b.   1.428 < μ < 1.652     c.  1.431  < μ <  1.649    d.   1.51 < μ <  1.57

Find the margin of error.

4. 99% confidence interval; n =  101 ;  =  27,  s =  5.2

1. 1.027                            b.  1.33                         c.  1.01                         d.  1.36

In the following problems use the given degree of confidence and sample statistics to construct a confidence interval for the population mean µ. Then interpret the results.

5. A laboratory tested twelve eggs and found that the average amount of cholesterol in each egg was 185 milligrams, with a sample standard deviation of 17.6 mg. Construct a 95% confidence interval for the mean cholesterol content in a typical egg.

1. 173.8 mg < μ < 196.2 mg
2. 173.7 mg < μ < 196.3 mg                 
3. 175.9 mg < μ < 194.1 mg
4. 173.9 mg < μ < 196.1 mg

Find the minimum sample size you should use to assure that your estimate of  will be within the required margin of error around the population proportion p.

1. Margin of error:  0.027;  confidence level: 93%;   is unknown

1. 1. 1124                             b.  1123                                    c.  2168                        d.  842
2. Margin of error:  0.025;  confidence level: 94%;  from a prior study,  is estimated to be 0.38.
   1. 1414                             b.   1332                       c.   1413                                    d.   1333

Solve the problem

3. Find the point estimate of the true proportion of people who are over 6 feet tall, if 184 people are randomly selected from a certain population and it is found that 41 of them are over 6 feet tall.
   1. 0.223                            b.   0.146                      c.   0.033                       d.   4.488

In the following three problems use the given degree of confidence and sample data to construct a confidence interval for the population proportion p. Then find the Point Estimate, and then interpret the results.

4. A survey of 976 voters in one state reveals that 478 favor approval of an issue before the legislature. Construct the 95% confidence interval for the true proportion of all voters in the state who favor approval.

4. 1. 0.440 < p < 0.540          b.  0.458 < p < 0.521      c.  0.487 < p < 0.493      d.  0.464 < p < 0.516
5. From the results in the problems above, we can say that
   1. At this Confidence Level it’s too close to call what the voters favor.
   2. More do not favor the proposal than favor it.
   3. The majority do not favor the approval.
   4. The majority favor approval.

The lengths (in mm) of a sample of 100 largemouth bass are given in the file LargemouthBass.csv in Digital appendices. (You can find this file under the “Digital Appendices” link on Blackboard.) Use R construct a frequency distribution table and histogram of these data.

Find the indicated Probability.

1. A bank’s loan office uses credit scores in their application process. The credit scores are normally distributed with a mean of 705 and a standard deviation of 55. Applicants are offered loans if their credit scores are above 670. Find the probability that a randomly selected applicant will be offered a loan.

1. 1. 0.2611                          b.   0.3811                    c.   0.7389                     d.  0.0703
2. Scores on a test are normally distributed with a mean of 72.5 and a standard deviation of 9.1. Find , the test score which separates the bottom 80% from the top 20%. Round to the nearest tenth.

1. 51.3                             b.   64.9                         c.   80.1                        d. 93.7

3. In one region, the September energy consumption levels for single-family homes are found to be normally distributed with a mean of 990 kWh and a standard deviation of 198 kWh. For a randomly selected home, find the probability that the September energy consumption level is between 1100 kWh and 1250 kWh.

1. 0.1926                          b.   0.3828                    c.   0.6178                     d. 0.8074

4. The lengths of human pregnancies are normally distributed with a mean of 268 days and a standard deviation of 15 days. What is the probability that a pregnancy lasts less than 270 days?

1. 0.4813                          b.   0.5517                    c.   0.50            d.  0.4483