Assume you wish to compare two distinct groups of people (e.g., men vs women; old vs young; those with college degree versus those without, those who shop online vs those who do not, etc.) Describe a situation where you would use one of the tests presented in this chapter, tests of goodness of fit, independence & multiple proportions. Identify the populations of interest; describe the research question; form the null and alternative hypotheses and the level of significance; the sample size and sampling procedure; and the test statistic and associated degrees of freedom.

Please provide realistic example

1. Due to a major effort to remove lead from the enviroment over the years, now only 9% of children in the U.S. are at risk of high blood levels of lead. Consider a random sample of 200 children.
a. Is it appropriate to use a normal approximation to the binomial distribution? Explain.

b. Determine the probability that between 10 and 25 children have high blood-lead levels.

1. In a study examining whether taking a statistics course influences students’ reasoning skill, a researcher first gave a reasoning task to 5 students who have never taken a statistics course, and then the students took a brief statistics lecture which lasted 3 hours. After the lecture, the same five students took the reasoning task again. Their performance scores are summarized in the table below.

Perform an appropriate statistical test and provide your conclusion on whether or not their reasoning performance are different before and after taking the STATS lecture.

2. In the above (#9), the same 5 students took the test twice, before and after the lecture. Reanalyze the above data as the data obtained from two sets of independent samples. Now please perform an appropriate statistical test to compare the means, pretending that two different (independent) groups of five people took the same test, one before and one after the lecture.

Power+, produces AA batteries used in remote-controlled toy cars. The mean life of these batteries follows the normal probability distribution with a mean of 27 hours and a standard deviation of 4.1 hours. As a part of its testing program, Power+ tests samples of 25 batteries. Use Appendix B.1 for the z-values. a. What can you say about the shape of the distribution of sample mean? Shape of the distribution is b. What is the standard error of the distribution of the sample mean? (Round the final answer to 4 decimal places.) Standard error c. What proportion of the samples will have a mean useful life of more than 28 hours? (Round the final answer to 4 decimal places.) Probability d. What proportion of the sample will have a mean useful life greater than 26.5 hours? (Round the final answer to 4 decimal places.) Probability e. What proportion of the sample will have a mean useful life between 26.5 and 28 hours? (Round the final answer to 4 decimal places.) Probability

A particular fruit's weights are normally distributed, with a mean of 652 grams and a standard deviation of 22 grams. If you pick 7 fruit at random, what is the probability that their mean weight will be between 624 grams and 637 grams

A large supermarket carries four qualities of ground beef. Customers are believed to purchase these four varieties with probabilities of 0.13, 0.27, 0.14, and 0.46, respectively, from the least to most expensive variety. A sample of 480 purchases resulted in sales of 48, 148, 74, and 210 of the respective qualities. Does this sample contradict the expected proportions? Use α = 0.05.

(a) Find the test statistic. (Round your answer to two decimal places.)


(ii) Find the p-value. (Round your answer to four decimal places.)

A program for generating random numbers on a computer is to be tested. The program is instructed to generate 100 single-digit integers between 0 and 9. The frequencies of the observed integers were as follows. At the 0.05 level of significance, is there sufficient reason to believe that the integers are not being generated uniformly?

(a) Find the test statistic. (Round your answer to two decimal places.)


(ii) Find the p-value. (Round your answer to four decimal places.)

Mercedes tires at Tracy's plant are produced in a manufacturing process and the diameter is VERY important factor that must be controlled.

From sample sizes of 10 tires produced each day, the mean sample of this diameter have been as follows:

a) What are the UCL_x, LCL_x ; use the following z value = 3

b) UCL_R , LCL_R , use the following z value = 3

1-Which type of bias can be minimized by masking the study subjects to the study hypothesis and by using diseased controls if conducting a case-control study?

2-Which type of bias can be minimized using sensitive and specific criteria to define the exposure and disease?

Consider the following results for independent samples taken from two populations.

Sample 1 Sample 2

n1 = 500 n2= 300

p1= 0.49 p2= 0.34

a. What is the point estimate of the difference between the two population proportions (to 2 decimals)?

b. Develop a 90% confidence interval for the difference between the two population proportions (to 4 decimals).
to

c. Develop a 95% confidence interval for the difference between the two population proportions (to 4 decimals).

Kay Mary, senior vice president for marketing at Terrapin Cosmetics, asked you to estimate, with 96% confidence, the proportion of all of the company’s customers who placed “large” orders, meaning over $200, in both January and February of 2019. To estimate the proportion, you selected a random sample of 845 customers. Of the customers in the sample, 165 placed large orders in both January and February of 2019. Please write the interval boundaries to THREE decimal places and interpret the interval.

• 6.32. Control charts for ¯xx¯ and R are in use with the following parameters:

  ¯¯¯xx¯ Chart	R Chart
  UCL = 363.0	UCL = 16.18
  Center line = 360.0	Center line = 8.91
  LCL = 357.0	LCL = 1.64

  The sample size is n = 9. Both charts exhibit control. The quality characteristic is normally distributed.

  1. What is the α-risk associated with the ¯xx¯ chart?
  2. Specifications on this quality characteristic are 358 ± 6. What are your conclusions regarding the ability of the process to produce items within specifications?
  3. Suppose the mean shifts to 357. What is the probability that the shift will not be detected on the first sample following the shift?
  4. What would be the appropriate control limits for the ¯xx¯ chart if the type I error probability were to be 0.01?
• 6.33. A normally distributed quality characteristic is monitored through use of an ¯xx¯ and an R chart. These charts have the following parameters (n = 4):

  ¯¯¯xx¯ Chart	R Chart
  UCL = 626.0	UCL = 18.795
  Center line = 620.0	Center line = 8.236
  LCL = 614.0	LCL = 0

  Both charts exhibit control.

  1. What is the estimated standard deviation of the process?
  2. Suppose an s chart were to be substituted for the R chart. What would be the appropriate parameters of the s chart?
  3. If specifications on the product were 610 ± 15, what would be your estimate of the process fraction nonconforming?
  4. What could be done to reduce this fraction nonconforming?
  5. What is the probability of detecting a shift in the process mean to 610 on the first sample following the shift (σ remains constant)?
  6. What is the probability of detecting the shift in part (e) by at least the third sample after the shift occurs?

6.35. The following ¯xx¯ and s charts based on n = 4 have shown statistical control:

1. Estimate the process parameters μ and σ.
2. If the specifications are at 705 ± 15, and the process output is normally distributed, estimate the fraction nonconforming.
3. For the ¯xx¯ chart, find the probability of a type I error, assuming σ is constant.
4. Suppose the process mean shifts to 693 and the standard deviation simultaneously shifts to 12. Find the probability of detecting this shift on the ¯xx¯ chart on the first subsequent sample.
5. For the shift of part (d), find the average run length.

Problem 5

a) Suppose that, in a random sample of 40 accounting students who had their second co-op term in W19, the sample mean and hourly wage and standard deviation were $20.10 and $3.15, respectively. Calculate a 95% confidence interval for the mean hourly wage of all accounting students with a second co-op term in W16. Interpret your interval.

b) Suppose that based on historic data accounting students on their first co-op term typically earn an average of $17.84 per hour. Does the data collected in part a) suggest that accounting students in their second co-op earn on average more than those on their first co-op? Perform a hypothesis test at a 10% level of significance to test this. Clearly state your conclusion.

1) Suppose the scores of students on a Statistics course are Normally distributed with a mean of 542 and a standard deviation of 98. What percentage of the students scored between 542 and 738 on the exam? (Give your answer to 3 significant figures.)

2) A new car that is a gas- and electric-powered hybrid has recently hit the market. The distance travelled on 1 gallon of fuel is normally distributed with a mean of 65 miles and a standard deviation of 6 miles. Find the probability of the following events:

A. The car travels more than 69 miles per gallon.

Probability =

B. The car travels less than 59 miles per gallon.

Probability =

C. The car travels between 59 and 68 miles per gallon.

Probability =

3)

(1 point) Suppose that X is normally distributed with mean 85 and standard deviation 20.

A. What is the probability that X is greater than 118?
Probability =

B. What value of XX does only the top 18% exceed?
X =

"Using data set 11-6; how many of the three factor interactions are stronger than the single factor ""B"""

11-6:

In the book Essentials of Marketing Research, William R. Dillon, Thomas J. Madden, and Neil H. Firtle discuss a research proposal in which a telephone company wants to determine whether the appeal of a new security system varies between homeowners and renters. Independent samples of 140 homeowners and 60 renters are randomly selected. Each respondent views a TV pilot in which a test ad for the new security system is embedded twice. Afterward, each respondent is interviewed to find out whether he or she would purchase the security system.

Results show that 25 out of the 140 homeowners definitely would buy the security system, while 9 out of the 60 renters definitely would buy the system.

(a) Letting p₁ be the proportion of homeowners who would buy the security system, and letting p₂ be the proportion of renters who would buy the security system, set up the null and alternative hypotheses needed to determine whether the proportion of homeowners who would buy the security system differs from the proportion of renters who would buy the security system.

(b) Find the test statistic z and the p-value for testing the hypotheses of part a. Use the p-value to test the hypotheses with α equal to .10, .05, .01, and .001. How much evidence is there that the proportions of homeowners and renters differ? (Round the intermediate calculations to 3 decimal places. Round your z value to 2 decimal and p -value to 3 decimal places.)

z=

p-value=

(c) Calculate a 95 percent confidence interval for the difference between the proportions of homeowners and renters who would buy the security system. On the basis of this interval, can we be 95 percent confident that these proportions differ? (Round your answers to confidence interval to 4 decimal places. Negative amounts should be indicated by a minus sign. )