Question 1: Determine whether the given description to an observational study or an experiment.

In a study of 424 children with particular disease, the subjects were monitored with an EEG while asleep.

Does the given description correspond to an observational study or an experiment?

A. The given description corresponds to an experiment.

B. The given description corresponds to an observational study.

C. The given description does not provide enough information to answer this question.

Question 2: Identify the type of sampling used (random, systematic, convenience, stratified, or cluster sampling) in the situation described below.

A man is selected by a marketing company to participate in a paid focus group. The company says that the man was selected because he was randomly chosen from all men in his tax bracket.

Which type of sampling did the marketing company use?

A. Systematic sampling, B. Random Sampling, C. Convenience Sampling, D. Cluster sampling, E. Stratified sampling

Question 3: Identify which type of sampling is used: random, systematic, convenience, stratified, or cluster.

A radio station asks its listeners to call in their opinion regarding the format of the morning show.

Which type of sampling is used?

A. Cluster, B. Stratified, C. Random, D. Systematic, E. Convenience

Question 4: Identify the type of sampling used (random, systematic, convenience, stratified, or cluster sampling) in the situation described below.

A woman experienced a tax credit. The tax department claimed that the woman was audited because everyone in four randomly selected districts was being audited.

Which type of sampling did the tax department use?

A. Cluster sampling

B. Systematic Sampling

C. Convenience Sampling

D. Random Sampling

E. Stratified Sampling

A researcher was interested in whether the female students who enrolled in her stats course were more interested in the topic than the males. The researcher obtained a random sample of 8 male and 8 female students and gathered their scores on an Interest in Statistical Topics (IST) Survey.

Girls’ IST scores: 21, 37, 22, 20, 22, 20, 22, 21

Boys’ IST scores: 20, 20, 20, 21, 21, 20, 23, 21

Test the researcher’s hypothesis using α =.05

Please show answer testing for equal variances.

A pharmaceutical company makes tranquilizers. It is assumed that the distribution for the length of time they last is approximately normal. Researchers in a hospital used the drug on a random sample of 9 patients. The effective period of the tranquilizer for each patient (in hours) was as follows: 2.6; 2.9; 3.0; 2.3; 2.3; 2.2; 2.8; 2.1; and 2.4. NOTE: If you are using a Student's t-distribution, you may assume that the underlying population is normally distributed. (In general, you must first prove that assumption, though.)

A. Round your answers to two decimal places.

x-bar =

s_x =

Enter an exact number as an integer, fraction, or decimal.

n =

Enter an exact number as an integer, fraction, or decimal.

n − 1 =

B. Which distribution should you use for this problem? (Enter your answer in the form z or t_df where df is the degrees of freedom.)

C. Construct a 95% confidence interval for the population mean length of time.

(i) State the confidence interval. (Round your answers to two decimal places.)

(ii) Sketch the graph.

a/2=

C.L.=

(iii) Calculate the error bound. (Round your answer to two decimal places.)

A sample of 17 small bags of the same brand of candies was selected. Assume that the population distribution of bag weights is normal. The weight of each bag was then recorded. The mean weight was 3 ounces with a standard deviation of 0.13 ounces. The population standard deviation is known to be 0.1 ounce. NOTE: If you are using a Student's t-distribution, you may assume that the underlying population is normally distributed. (In general, you must first prove that assumption, though.)

A. Find the following. (Round your answers to two decimal places.)

(i)    x-bar =
(ii)   σ =

(iii)   s_x =

B. Which distribution should you use for this problem? (Round your answers to three decimal places.)

X-bar ~ ___ (_______ ,_______)

C. Construct a 90% confidence interval for the population mean weight of the candies.

(i) State the confidence interval. (Round your answers to three decimal places.)

(ii) Sketch the graph.

a/2=

C.L.=

(iii) Calculate the error bound. (Round your answer to three decimal places.)

D. Construct a 98% confidence interval for the population mean weight of the candies.

(i) State the confidence interval. (Round your answers to three decimal places.)

(ii) Sketch the graph.

a/2=

C.L. =

(iii) Calculate the error bound. (Round your answer to three decimal places.)

The following are the temperatures of a group of children diagnosed with chicken pox. Use the data below to answer questions 9 – 20.

98 102 98 100 101 99 99 100 102 101

9. What is the sample mean temperature? a. 100.0b. 98.5 c. 99.2 d. 101.1

10. What is the sample median? a. 100

11. b. 99 c. 98 d. 97

12. What is the variance? a. 2.2

13. b. 2 c. 2.6 d. 2.4

14. What is the 25th percentile?a. 97

15. b. 98 c. 99 d. 100

16. What is the 75th percentile? a. 101

    b. 102 c. 100 d. 103

17. True or False: 97 is an outlier.

18. Choose from the following relative frequency histograms that correspond with the temperature

    data broken into 3 groups, Group A: 97.0 – 99.9, Group B: 100.0 – 101.9, Group C: 102.0 – 103.9

A statistical program is recommended.

The owner of Showtime Movie Theaters, Inc., would like to predict weekly gross revenue as a function of advertising expenditures. Historical data for a sample of eight weeks follow.

a) Predict weekly gross revenue (in dollars) for a week when $3,300 is spent on television advertising and $1,500 is spent on newspaper advertising. (Round your answer to the nearest cent.)

$

b) Predict weekly gross revenue (in dollars) for a week when $3,500 is spent on television advertising and $1,300 is spent on newspaper advertising. (Round your answer to the nearest cent.)

$  

The Pawnee Rangers, a boys-only wilderness club, and the Pawnee Goddesses, a girls-only wilderness club, went on a joint weekend camping trip with their respective troop leaders Ron Swanson and Leslie Knope. Leslie claims that her club (the Pawnee Goddesses) is better than Ron’s club.  You may assume that the members who went on the camping trip are representative samples of their respective clubs. Please assume that “boy” and “girl” refer to each child’s self-identified  gender.

During the weekend trip, Leslie proposes that the two clubs have a fishing competition to see if her club is better. To measure club superiority, Leslie is interested in comparing the long-run  proportions of club members who can catch a fish within one hour. After fishing for one hour, each person caught at most one fish (either no fish or one fish). The results are shown in the two-way table below.

Define the following notation:

pR: the long-run proportion of Pawnee Rangers who can catch a fish within one hour

pG: the long-run proportion of Pawnee Goddesses who can catch a fish within one hour

Leslie used the two-sample z-test to compute a p-value of 0.0929, but Ron believes that Leslie's p-value is not valid. If all other things remain the same, how can Leslie fix the issue with her analysis?

Select one:

Ron is incorrect, all the conditions are satisfied for Leslie's analysis to be valid.

Increase the number of Pawnee Goddesses in the sample.

Increase the number of Pawnee Rangers in the sample.

Use the two-sample t-test instead of the z-test.

A health organization collects data on an individuals daily intake of selected nutrients and on their income level. The protein intake (in grams) over a 24hr period was determined for independent random samples random samples of 40 adults with income below the poverty level and 50 adults with income above the poverty level. The results:

a) Complete the following to construct a 95% confidence interval for the amount by which true mean protein intake for adults having income above the poverty level exceeds that of adults having income below the poverty level

Parameter of interest: _____________

Degrees of freedom:

Standard error (to 5 decimal places):

Critical value t*:

Confidence interval (to 3 decimal places):

Conclusion:

b) Assuming that all of the results remained unchanged, for what level of confidence C would a margin of error of 5 grams be obtained when calculating a symmetric 100(1-α)% confidence interval? Express your final answer to 2 decimal places.

10.30  Grade inflation. The average undergraduate GPA for American colleges and universities was estimated based on a sample of institutions that published this information.¹³ Here are the data for public schools in that report:

Do the following by hand or with a calculator and verify your results with a software package.

1. (a) Make a scatterplot that shows the increase in GPA over time. Does a linear increase appear reasonable?

2. (b) Find the equation of the least-squares regression line for predicting GPA from year. Add this line to your scatterplot.

3. (c) Compute a 95% confidence interval for the slope and summarize what this interval tells you about the increase in GPA over time.

The net weekly sales for a small business follows a normal distribution with a mean of 588 dollars and standard deviation of 107 dollars.

Calculate each of the following.

In each case, round your response to at least 4 decimal places.

a) What is the probability that in a randomly selected day, the business will do no more than 674 dollars in net sales?

b) Suppose 16 days are randomly selected. What is the probability that the average net sales the business will do is at least 568 dollars?

c) What is the probability that for 16 randomly selected days, the business will have a mean net sales between 573 dollars and 643 dollars?

Construct a frequency distribution for the motor fuel octane data below using RStudio:

Rating
88.5
94.7
84.3
90.1
89
89.8
91.6
90.3
90
91.5
89.9
98.8
88.3
90.4
91.2
90.6
92.2
87.7
91.1
86.7
93.4
96.1
89.6
90.4
91.6
90.7
88.6
88.3
94.2
85.3
90.1
89.3
91.1
92.2
83.4
91
88.2
88.5
93.3
87.4
91.1
90.5
100.3
87.6
92.7
87.9
93
94.4
90.4
91.2
86.7
94.2
90.8
90.1
91.8
88.4
92.6
93.7
96.5
84.3
93.2
88.6
88.7
92.7
89.3
91
87.5
87.8
88.3
89.2
92.3
88.9
89.8
92.7
93.3
86.7
91
90.9
89.9
91.8
89.7
92.2

You need to use R. Please show all work

Consumers Union provides ratings on a large variety of consumer products. They use sophisticated testing methods as well as surveys of their members to create these ratings.

One recent article rated laundry detergents on a scale from 1 to 100. Here are the ratings along with the price per load, in cents, for 24 laundry detergents:

Use these data to compute the correlation between rating and the price per load.

(Use decimal notation. Give your answer to three decimal places.)

The Ankle Brachial Index​ (ABI) compares the blood pressure of a​ patient's arm to the blood pressure of the​ patient's leg. A healthy ABI is 0.9 or greater. In a​ study, researchers obtained the ABI of 187 women with arterial disease. The results were a mean ABI of 0.89 with a standard deviation of 0.13 . At the 10 ​% significance​ level, do the data provide sufficient evidence to conclude​ that, on​ average, women with arterial disease have an unhealthy​ ABI?

Name the test or tests that are appropriate to answer the following questions.

(a) Whether the slope of the best fit line is different from zero?

(b) Whether the slope of the best fit line is greater than 1?

(c) Whether the intercept is different from zero?

(d) Whether the intercept is less than - 3?

These questions are related to Regression. Please explain why these tests would be best so I can understand.

The Food Marketing Institute and Nielsen reported that 49% of U.S. consumers shop for consumer package goods products online. Assume the population proportion is p=0.49 and a sample of 500 consumers will be selected from the population.

Calculate the expected value and the standard error for the sampling distribution of p ̅, the sample proportion of consumers who shop for consumer package goods product online.

Describe the sampling distribution of p ̅. Draw a graph of this probability distribution with its mean and standard deviation.

What is the probability that the sample proportion will be greater than 0.52?

What is the probability that the sample proportion will be within ±0.02 of the population proportion?

Answer part d for a sample of 1000 households.