You wish to test the following claim ( H a ) at a significance level of α = 0.02 . H o : μ = 61.5 H a : μ ≠ 61.5 You believe the population is normally distributed, but you do not know the standard deviation. You obtain a sample of size n = 15 with mean ¯ x = 75.7 and a standard deviation of s = 15.7 . What is the test statistic for this sample? test statistic = Round to 3 decimal places What is the p-value for this sample? p-value = Use Technology Round to 4 decimal places. The p-value is... less than (or equal to) α greater than α This test statistic leads to a decision to... reject the null accept the null fail to reject the null As such, the final conclusion is that... There is sufficient evidence to warrant rejection of the claim that the population mean is not equal to 61.5. There is not sufficient evidence to warrant rejection of the claim that the population mean is not equal to 61.5. The sample data support the claim that the population mean is not equal to 61.5. There is not sufficient sample evidence to support the claim that the population mean is not equal to 61.5.

The following data represent a company's yearly sales volume and its advertising expenditure over a period of 8 years.

                                                (Y)                                          (X)        

Sales in millions                     Advertising in ($10,000)

                                                15                                            32

                                                16                                            33

                                                18                                            35

                                                17                                            34

                                                16                                            36

(a) Develop a scatter diagram of sales versus advertising and explain what it shows regarding the relationship between sales and advertising.

(b) Use the method of least squares to compute an estimated regression line between sales and advertising by computing b0 and b1.

(c) If the company's advertising expenditure is $400,000, what are the predicted sales? Give the answer in dollars.

(d) What does the slope of the estimated regression line indicate?

(e) Compute the coefficient of determination for the estimated regression equation you got in the previous in-class problem.

(f) Interpret the meaning of the value of the coefficient of determination that you found in d. Be very specific.

(g) Perform a t test and determine whether or not X and Y are related. Let it = 0.05.

(h) Perform an F test and determine whether or not X and Y are related. Let it = 0.05.

Business Statistics

Data Analysis for Managers making decisions

You manage a line of consumer products and want to change your marketing campaign. You decide that you want to test a new campaign against the existing one to see if the new one is any better. How would you design the test? What sort of data would you collect? Would you be using a dependent or independent variable? Would you use a simple regression analysis or a multiple regression analysis? Justify your answer

Counting

Jack has a collection of 10 pairs of gloves in his wardrobe. Before a business trip, he has to pack his luggage, and he selects 8 gloves, without looking at them. We assume that any set of 8 gloves is equally likely to be chosen. Find the probability that these 8 gloves do not include any matching pair of gloves, that is, that there are no two (left and right) gloves, coming from the same pair.

To see if a spinner that is divided into 100 equal sections labeled 1 to 100 is fair, a researcher spins the spinner 1000 times and records the result. Let X represent the outcome. The table below shows the probability distribution of the data. Find the mean and the standard deviation of the probability distribution using Excel. Round the mean and standard deviation to two decimal places.

A psychologist specializing in marriage counseling claims that, among all married couples, the proportion p for whom her communication program can prevent divorce is at least 76%. In a random sample of 225 married couples who completed her program, 168 of them stayed together. Based on this sample, can we reject the psychologist's claim at the 0.05 level of significance?Perform a one-tailed test. Then fill in the table below.Carry your intermediate computations to at least three decimal places and round your answers as specified in the table. (If necessary, consult a list of formulas.)

Problem #4  Mike Dreskin manages a large Los Angeles movie theater complex called Cinema I, II, III, and IV. Each of the four auditoriums plays a different film; the schedule is set so that starting times are staggered to avoid the large crowds that would occur if all four movies started at the same time. The theater has a single ticket booth and a cashier who can maintain an average service rate of 280 movie patrons per hour. Service times are assumed to follow an exponential distribution. Arrivals on a typically active day are Poisson distributed and average 210 per hour.

To determine the efficiency of the current ticket operation, Mike wishes to examine several queue operating characteristics.

(a) Find the average number of moviegoers waiting in line to purchase a ticket.

(b) What percentage of the time is the cashier busy?

(c) What is the average time that a customer spends in the system?

(d) What is the average time spent waiting in line to get to the ticket window?

(e) What is the probability that there are more than two people in the system?

10-1

Researchers in a populous country contacted more than​ 25,000 inhabitants aged 22 years to see if they had finished high​ school; 81.7%

of the 12,858 males and 80.1​% of the 12,957 females indicated that they had high school diplomas.

​a) What assumptions are necessary to satisfy the conditions necessary for​ inference?

​b) Create a 90​% confidence interval for the difference in graduation rates between males and​ females,

p Subscript males Baseline minus p Subscript femalespmales−pfemales.

​c) Interpret your confidence interval.

​d) Is there evidence that boys are more likely than girls to complete high​ school?

In order to determine the relationship between the price of an item (X) and the quantity sold (Y), the price of the item was varied over 10 consecutive days. The following data are the results of the study.

          SX = 60, SX² = 436, SY = 63, SY² = 469, SXY = 335, SSR = 24.3289

1. Develop the least squares estimated regression line.
2. Calculate SSE.
3. Perform a t test and determine whether or not the slope is significantly different from zero. Let a = 0.05.  
4. At a = 0.05, perform an F test to determine if the regression model is significant.
5. Develop a 90% confidence interval for estimating the mean quantity sold for those days when the price was $6.

Suppose 229 subjects are treated with a drug that is used to treat pain and 53 of them developed nausea. Use a 0.01 significance level to test the claim that more than 20​% of users develop nausea.

Identify the test statistic for this hypothesis test.
The test statistic for this hypothesis test is ?
​(Round to two decimal places as​ needed.)
Identify the​ P-value for this hypothesis test.
The​ P-value for this hypothesis test is ?

Identify the conclusion for this hypothesis test.
A.
Reject Upper H 0. There is sufficient evidence to warrant support of the claim that more than 20​% of users develop nausea.
B.
Reject Upper H 0. There is not sufficient evidence to warrant support of the claim that more than 20​% of users develop nausea.
C.
Fail to reject Upper H 0. There is not sufficient evidence to warrant support of the claim that more than 20​% of users develop nausea.
.D.
Fail to reject Upper H 0. There is sufficient evidence to warrant support of the claim that more than 20​% of users develop nausea.

In a study relating consumption expenditure (Y) on income (X2) and wealth (X3) based on 10 observations , the following equation was obtained

Yhat = 24.337 + 0.08764X2 - 0.0349X3

     SE   (6.2801)    (0.31438)   (0.0301)

       t    (3.875)      (2.7726)     (-1.1595)               

i) In your opinion, what type of problem takes in this result? Explain it

ii)   What are the practical consequences of this problem?

iii) What are the theoretical of this problem

iv) How to detect this problem?

v)In your judgement, what to do to remove this problem?

vi) How do we remedy this problem

Please do the math by hand, do not use a program, I need to see the procedure, the answer itself is less important.

Comparison of peak expiratory flow rate (PEFR) before and after a walk on a cold winter's day for a random sample of 9 asthmatics. Use the following data to determine if the patients conditioned changed after a walk. Present your results and make some interpretations.

Data for age (in years) and price (in hundreds of dollars) for a particular brand of car are provided in the accompanying data table. Presume that the assumptions for regression inferences have been met. Complete parts (a) through (d) below using the given data.

X (age) 6, 6, 6, 2, 2, 5, 4, 5, 1, 4

Y (price) 289, 280, 293, 428, 382, 315, 355, 326, 423, 322

A) Obtain a point estimate for the mean price of all 3-year old cars of this brand.

B) Determine a 90% confidence interval for the mean price of all 3-year old cars of this brand.

C) Find the predicted price of a 3-year old car of this brand.

D) Determine a 90% prediction interval for the price of a 3-year old car of this brand.

Phil wishes to compare the weights of professional athletes to the weights of non-professional athletes. Phil completes a simple random sample of professional athletes and records his results in pounds:

125  147  240  186  156  205  248  152  199  207  176

Phil also completes a simple random sample of non-professional athletes and records his results in pounds:

151  161  139  128  149  160  201  173

The samples are independent and come from normally distributed populations. Use the p-value method and a 2% significance level to test the claim that the mean weights of professional and non-professional athletes are the same.

1) What population parameter is being tested? (mean, proportion etc)
2) How many populations are being tested?
3) Calculate the sample mean weight of professional athletes (round to the nearest ten-thousandth).
4) What is the claim? (At this point, you should have already selected the formula that will be used to calculate the test statistic and written it in the test statistic box.) What is the alternative hypothesis?
5) What is the test statistic (rounded to the nearest thousandth)?
6) The critical region is best described as (right/left/2)
7) What is the largest lower bound of the p-value from the table (rounded to the nearest hundredth) or the value of the p-value found using technology (rounded to the nearest ten-thousandth?)
8) What is the significance level (expressed as a decimal)?
9) What is the statistical conclusion?