A student stated: “I fail to see why the response function needs to be constrained between 0 and 1 when the response variable is binary and has a Bernoulli distribution. The fit to 0, 1 data will take care of this problem for any response function.” Comment.

How do you interpret t statistic? Please give examples and describe how to interpret t statistic in detail

What does a high/low t statistic mean?

6. What are the three bits of information that the t table needs in order to use it?

10. a. Perform a test with the following scores: Population mean = 94, M=100 and the SEM=7.
b. Consult the t table to obtain a critical value for the outcome using an alpha level of α=.05, for a two tailed test and with a degree of freedom of df=7.
c. Would the t value you got be significant if doing a true test?

12. What are the three parts of the t test (or any statistical test) that you need to report when using APA standards?

16. a. If the degrees of freedom for the one sample t test was listed as df=14. How many participants were in the study?
b. How many degrees are free to vary in any one group?

. A bank has recently begun a new credit program. Customers meeting a certain credit requirement can obtain a credit card accepted by participating area merchants that carries a discount. Past data show that about 35% of all applicants for this card are rejected. If we let X represent the number of applicants who are approved for this credit card, the probabilities for the values of X can be calculated using the binomial probability distribution. Please answer the following questions based on the information given in this problem.

a. If 15 individuals apply for the credit card today what is the probability that none of them will be rejected? Show your work.                                           (1 point)                                                                                                                     

b. If 15 individuals apply for the credit card today what is the probability of at most 5 of them being rejected? Show your work.                                      (2 points)     

c. If 15 individuals apply for the credit card today what is the probability of more than 12 of them being approved? Show your work.                         (2 points)           

d. If 15 individuals apply for the credit card today what is the probability of less than half of them being approved? Show your work.                      (2 points)                                                                                                                                                                                                                                                  

e. If 15 individuals apply for the credit card today what is the probability of at least 6 of them being rejected? Show your work.                                          (2 points)           

f. How many rejections are expected out of the 15 applications?       (1 point)     

g. Calculate and interpret the standard deviation for the number of approvals out of the next 15 applications for the credit card. Show your work

Show how ( Chi-Square) can be applied, and how it may be used in any industry of your choosing. Provide a brief description of what the “Chi-Square” distribution is used for, then provide the example, and then tell what that example showed.

(Note: The answer has to be typed, not hand written nor in a picture.) Thank you.

1. Finally, you have been asked to compare the mean ages of the supporters of the candidate in various sectors of the country. Random samples of supporters of the candidate are selected from five geographic areas. The data that has been collected is shown in appendix four below. At the 5% level of significance, are there any differences in the mean ages of the supporters of the candidate based on their residencies? If you do find any differences in the mean ages, do the work necessary to find where those differences lie. As a further part of your work, perform the necessary test to ascertain whether the necessary quality of homogeneity of variances exists.

Appendix Four:

                                                                      Region

            Supporter      North       East         South              West               Midwest

       1              23             36              45                 22                      40

       2              66             50              48                  51                      75

       3              43             40              29                  52                      65

       4              70             28              30                  31                      30

       5              60             26              38                35                      67

       6              49             34              87                65                      78

       7              54             59            20                 19                      67

       8              64           51              26                29                      76

       9              54             50              39                43                      44

      10             60             42              38                54                      61

      11             70             58              50                48                      70

      12             49             48              29                18                      90

      13             38             37              21                34                      78

      14             40             31              29                30                      69

      15             49             52              40                50                      28

A market research consultant hired by a leading soft-drink company wants to determine the proportion of consumers who favor its low-calorie drink over the leading competitor's low-calorie drink in a particular urban location. A random sample of 250 consumers from the market under investigation is provided in the file P08_17.xlsx.

a. Calculate a 95% confidence interval for the proportion of all consumers in this market who prefer this company's drink over the competitor's. Round your answers to three decimal places, if necessary.

Count = 134

n = 250

Suppose that the amount of time that students spend studying in the library in one sitting is normally distributed with mean 43 minutes and standard deviation 17 minutes. A researcher observed 43 students who entered the library to study. Round all answers to 4 decimal places where possible.

What is the distribution of X?X ~ N(,)

What is the distribution of x¯? x¯ ~ N(,)

What is the distribution of ∑x? ∑x ~ N(,)

If one randomly selected student is timed, find the probability that this student's time will be between 41 and 44 minutes.

For the 43 students, find the probability that their average time studying is between 41 and 44 minutes.

Find the probability that the randomly selected 43 students will have a total study time more than 1978 minutes.

The top 20% of the total study time for groups of 43 students will be given a sticker that says "Great dedication". What is the least total time that a group can study and still receive a sticker? _minutes

The mean cost of domestic airfares in the United States rose to an all-time high of $375 per ticket. Airfares were based on the total ticket value, which consisted of the price charged by the airlines plus any additional taxes and fees. Assume domestic airfares are normally distributed with a standard deviation of $120. Use Table 1 in Appendix B.

a. What is the probability that a domestic airfare is $540 or more (to 4 decimals)?

b. What is the probability that a domestic airfare is $250 or less (to 4 decimals)?

c. What if the probability that a domestic airfare is between $310 and $490 (to 4 decimals)?

d. What is the cost for the 2% highest domestic airfares? (rounded to nearest dollar)

Suppose that a multiple regression model was developed with a sample of data of size 190 and 13 independent variables. One of the 13 independent variables is a qualtiative variable with 6 levels for which necessary dummy variables were defined.

a)

The following is a partially complete ANOVA table for the Multiple Regression analysis. Round Answer to 4 Decimal Places

An organization surveyed 1,100 adults and​ asked, "Are you a total abstainer​ from, or do you on occasion​ consume, alcoholic​ beverages?" Of the 1,100 adults​ surveyed, 363 indicated that they were total abstainers. Sixty years​ later, the same question was asked of 1,100 adults and 435 indicated that they were total abstainers. Has the proportion of adults who totally abstain from alcohol​ changed? Use the a equals 0.=0.10 level of significance.

A drapery store manager was interested in determining whether a new employee can install vertical blinds faster than an employee who has been with the company for two years. The manager takes independent samples of 10 vertical blind installations of each of the two employees and computes the following information.

a) State the appropriate null and alternative hypotheses to test whether the new employee installs vertical blinds faster, on the average, than the veteran employee.

b) Calculate the pooled estimate of the common variance

c) Calculate the value of the test statistic

d) Set up the appropriate rejection region for the hypotheses in question i) assuming a = 0.05.

e) What is the appropriate conclusion?

In a survey of 624 males ages​ 18-64, 397 say they have gone to the dentist in the past year.

Construct​ 90% and​ 95% confidence intervals for the population proportion. Interpret the results and compare the widths of the confidence intervals. If​ convenient, use technology to construct the confidence intervals.

(a) The​ 90% confidence interval for the population proportion p is (___,___)
(Round to three decimal places as​ needed.)

(b) The​ 95% confidence interval for the population proportion p is (____,____)
​(Round to three decimal places as​ needed.)

(c) Interpret your results of both confidence intervals:

1. With the given​ confidence, it can be said that the population proportion of males ages​ 18-64 who say they have gone to the dentist in the past year is between the endpoints of the given confidence interval.

2. With the given​ confidence, it can be said that the sample proportion of males ages​ 18-64 who say they have gone to the dentist in the past year is between the endpoints of the given confidence interval.

3. With the given​ confidence, it can be said that the population proportion of males ages​ 18-64 who say they have gone to the dentist in the past year is not between the endpoints of the given confidence interval.

(d) Which interval is​ wider?

The​ 90% confidence interval

or

The​ 95% confidence interval

One factor in rating a National Hockey League team is the mean weight of its players. A random sample of players from the Detroit Red Wings was obtained. The weight (in pounds) of each player was carefully measured, and the resulting data have a sample size of 16 with a sample mean of 202 pounds and a sample standard deviation of 11.6 pounds. Assume that the distribution of the weights is normal. Please use 4 decimal places for all critical values.

(0.5 pts.) a) Find the 95% confidence interval for the true mean weight of the players from the Detroit Red Wings.

(0.5 pts.) b) Calculate the 95% lower bound of the true mean weight of the players from the Detroit Red Wings.

(1 pt.) Interpret your answer above (part b).

(1 pt.) c) Why is the lower limit from part a) different from the lower bound in part b)? Please explain your answer by listing the symbols that are different between parts a) and b) and explain why the symbols are used.

d) The 95% confidence interval of the weights for the Boston Bruins is (194.19, 205.81). If the true mean weights for the two teams are different, then it is likely that there will be a more physical game when the two teams meet. Is there any evidence to suggest that the true mean player weight of Detroit is different from that of Boston? Please explain your answer.