1.       A   university   researcher   is   interested   in   whether   recent   recruitment   efforts   have   changed   the   type   of   students   admitted   to   the   university.   To   test   this,   she   randomly   selects   50   freshmen   from   the   university   and   records   their   high   school   GPA.   The   mean   is   2.90   with   a   standard   deviation   of   0.70.   The   researcher   also   knows   that   the   mean   high   school   GPA   of   all   freshmen   enrolled   at   the   university   five   years   ago   was   2.75   with   a   standard   deviation   of   0.36.   The   researcher   wants   to   know   if   the   high   school   GPA   of   current   freshmen   at   the   university   is   different   than   that   of   freshmen   from   five   years   ago.  
   (a)   What   are   the   null   and   alternative   hypotheses   in   this   study   (stated   mathematically)?  
   (b)   Should   the   researcher   use   a   one-tailed   or   a   two-tailed   test?  
   (c)   Compute   the   appropriate   test   statistic   for   testing   the   hypothesis.  
   (d)   Using   α   =   0.05,   what   do   you   conclude   about   the   high   school   GPA   of   current   freshman?   Be   sure   to   include   a   discussion   of   the   critical   value   in   your   answer.  
   (e)   What   type   of   error   might   the   researcher   be   making   in   part   (d)?  
  
   2.   A   researcher   believes   that   smoking   worsens   a   person’s   sense   of   smell.   To   test   this,   he   takes   a   sample   of   25   smokers   and   gives   them   a   test   of   olfactory   sensitivity.   In   this   test,   higher   scores   indicate   greater   sensitivity.   For   his   sample,   the   mean   score   on   the   test   is   15.1   with   a   standard   deviation   of   1.2.   The   researcher   knows   the   mean   score   in   the   population   is   15.5,   but   the   population   standard   deviation   is   unknown.  
   (a)   What   are   the   null   and   alternative   hypotheses   in   this   study   (stated   mathematically)?  
   (b)   Should   the   researcher   use   a   one-tailed   or   a   two-tailed   test?  
   (c)   Compute   the   appropriate   test   statistic   for   testing   the   hypothesis.  
   (d)   Using   α   =   0.01,   do   you   conclude   that   smoking   affects   a   person’s   sense   of   smell?   Be   sure   to   include   a   discussion   of   the   critical   value   in   your   answer.  
   (e)   What   type   of   error   might   the   researcher   be   making   in   part   (d)?  
  

The following table shows age distribution and location of a random sample of 166 buffalo in a national park. Age Lamar District Nez Perce District Firehole District Row Total Calf 14 12 15 41 Yearling 13 11 9 33 Adult 35 30 27 92 Column Total 62 53 51 166 Use a chi-square test to determine if age distribution and location are independent at the 0.05 level of significance. (a) What is the level of significance? State the null and alternate hypotheses. H0: Age distribution and location are not independent. H1: Age distribution and location are not independent. H0: Age distribution and location are independent. H1: Age distribution and location are independent. H0: Age distribution and location are independent. H1: Age distribution and location are not independent. H0: Age distribution and location are not independent. H1: Age distribution and location are independent. (b) Find the value of the chi-square statistic for the sample. (Round the expected frequencies to at least three decimal places. Round the test statistic to three decimal places.) Are all the expected frequencies greater than 5? Yes No What sampling distribution will you use? Student's t chi-square binomial uniform normal What are the degrees of freedom? (c) Find or estimate the P-value of the sample test statistic. (Round your answer to three decimal places.) p-value > 0.100 0.050 < p-value < 0.100 0.025 < p-value < 0.050 0.010 < p-value < 0.025 0.005 < p-value < 0.010 p-value < 0.005 (d) Based on your answers in parts (a) to (c), will you reject or fail to reject the null hypothesis of independence? Since the P-value > α, we fail to reject the null hypothesis. Since the P-value > α, we reject the null hypothesis. Since the P-value ≤ α, we reject the null hypothesis. Since the P-value ≤ α, we fail to reject the null hypothesis. (e) Interpret your conclusion in the context of the application. At the 5% level of significance, there is sufficient evidence to conclude that age distribution and location are not independent. At the 5% level of significance, there is insufficient evidence to conclude that age distribution and location are not independent.

Consider the experimental results for the following randomized block design. Make the calculations necessary to set up the analysis of variance table.

Use α = 0.05 to test for any significant differences.

State the null and alternative hypotheses.

H₀: μ_A ≠ μ_B ≠ μ_C
H_a: μ_A = μ_B = μ_C

H₀: At least two of the population means are equal.
H_a: At least two of the population means are different.    

H₀: μ_A = μ_B = μ_C
H_a: μ_A ≠ μ_B ≠ μ_C

H₀: μ_A = μ_B = μ_C
H_a: Not all the population means are equal.

H₀: Not all the population means are equal.
H_a: μ_A = μ_B = μ_C

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

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

p-value =

State your conclusion.

Reject H₀. There is sufficient evidence to conclude that the means of the three treatments are not equal.

Reject H₀. There is not sufficient evidence to conclude that the means of the three treatments are not equal.    

Do not reject H₀. There is not sufficient evidence to conclude that the means of the three treatments are not equal.

Do not reject H₀. There is sufficient evidence to conclude that the means of the three treatments are not equal.

A magazine collects data each year on the price of a hamburger in a certain fast food restaurant in various countries around the world. The price of this hamburger for a sample of restaurants in Europe in January resulted in the following hamburger prices (after conversion to U.S. dollars).

5.19 4.92 4.04 4.69 5.25 4.64

4.17 4.99 5.12 5.52 5.36 4.60

The mean price of this hamburger in the U.S. in January was $4.61. For purposes of this exercise, assume it is reasonable to regard the sample as representative of these European restaurants. Does the sample provide convincing evidence that the mean January price of this hamburger in Europe is greater than the reported U.S. price? Test the relevant hypotheses using α = 0.05. (Use a statistical computer package to calculate the P-value. Round your test statistic to two decimal places and your P-value to three decimal places.)

t = _____

P-value =_______

What is the purpose of a residual analysis? Which diagrams have to be included. Why? (4 Marks

Medical research has shown that repeated wrist extension beyond 20 degrees increases the risk of wrist and hand injuries. Each of 24 students at a university used a proposed new computer mouse design. While using the mouse, each student's wrist extension was recorded. Data consistent with summary values given in a paper are given. Use these data to test the hypothesis that the mean wrist extension for people using this new mouse design is greater than 20 degrees. (Use α = 0.05. Use a statistical computer package to calculate the P-value. Round your test statistic to two decimal places and your P-value to three decimal places.)

26 28 25 24 26 27 27 25 25 25 27 28

22 27 25 28 26 24 31 27 28 26 26 27

t = ____________

P-value =_____________

Television viewing reached a new high when the global information and measurement company reported a mean daily viewing time of 8.35 hours per household. Use a normal probability distribution with a standard deviation of 2.5 hours to answer the following questions about daily television viewing per household. a. What is the probability that a household views television between 4 and 8 hours a day (to 4 decimals)? b. How many hours of television viewing must a household have in order to be in the top 5% of all television viewing households (to 2 decimals)? c. What is the probability that a household views television more than 5 hours a day (to 4 decimals)?

14_ The average chocolate chip cookie contains 110 calories. A random sample of 15 different brands of chocolate chip cookies found that the average amount of calories was 127 calories with a sample deviation of 6.23 calories. At .01 level of significance, test the hypothesis that the average calories for chocolate chip cookies greater than 110.

What are your null (H0) and alternative (H1) hypotheses?

What is the z or t score for step 2

What is the statistic value for step 3?

What is the decision step 4?

Per capita income depends on the savings rate of the country: e.g. countries who save more end up with a higher standard of living. To test this theory, you collect data from the Penn World Tables on GDP per worker relative to the United States (RelProd) in 1990 and the average investment share of GDP from 1980-1990 (SK), remembering that investment equals saving. The regression results (using heteroskedasticity-robust standard errors) are:

RelProd = −0.08 + 2.44 ×SK , R2 = 0.46, SER = 0.21 (0.04) (0.26)

(Q4) Interpret the regression results carefully (including both coefficients and the R2) and Calculate the t-statistics to determine whether the two coefficients are significantly different from zero. Justify the use of a one-sided or two-sided test.

Sales personnel for Skillings Distributors submit weekly reports listing the customer contacts made during the week. A sample of 85 weekly reports showed a sample mean of 19.5 customer contacts per week. The sample standard deviation was 5.5. Provide 90% and 95% confidence intervals for the population mean number of weekly customer contacts for the sales personnel.

a. 90% confidence interval, to 2 decimals:

b. 95% confidence interval, to 2 decimals:

In the casino game roulette, the probability of winning with a bet on red is p = 17/38. Let Y equal the number of winning bets out of 1000 independent bets that are placed. Find P(Y > 500), approximately.

Show all your work.

Because of safety considerations, in May 2003 the Federal Aviation Administration (FAA) changed its guidelines for how small commuter airlines must estimate passenger weights. Under the old rule, airlines used 180 pounds as a typical passenger weight (including carry-on luggage) in warm months and 185 pounds as a typical weight in cold months.

A journal reported that an airline conducted a study to estimate average passenger plus carry-on weights. They found an average summer weight of 183 pounds and a winter average of 190 pounds. Suppose that each of these estimates was based on a random sample of 100 passengers and that the sample standard deviations were 20 pounds for the summer weights and 21 pounds for the winter weights.

(a) Construct a 95% confidence interval for the mean summer weight (including carry-on luggage) of this airline's passengers. (Round your answers to three decimal places.) Incorrect: -_______________ , Incorrect:____________________

Interpret a 95% confidence interval for the mean summer weight (including carry-on luggage) of this airline's passengers. Correct: Your answer is correct.

(b) Construct a 95% confidence interval for the mean winter weight (including carry-on luggage) of this airline's passengers. (Round your answers to three decimal places.)

Incorrect: _______________. , Incorrect: ______________________

Interpret a 95% confidence interval for the mean winter weight (including carry-on luggage) of this airline's passengers.

There is a 95% chance that the true mean winter weight (including carry-on luggage) of this airline's passengers is one of these two values.

There is a 95% chance that the true mean winter weight (including carry-on luggage) of this airline's passengers is between these two values.

We are 95% confident that the true mean winter weight (including carry-on luggage) of this airline's passengers is directly in the middle of these two values.

There is a 95% chance that the true mean winter weight (including carry-on luggage) of this airline's passengers is directly in the middle of these two values.

We are 95% confident that the true mean winter weight (including carry-on luggage) of this airline's passengers is between these two values. Correct: Your answer is correct.

1. In a Gallup poll, 1011 adults were randomly selected and asked if they consume alcoholic beverages. Of this sample, 64% said they did.
   1. Check requirements before computing confidence interval
   2. If requirements are met, use StatCrunch to obtain a 90% confidence interval for the proportion of all adults who consume alcoholic beverages.
   3. c. Write interpretation of the confidence interval.

A prescription drug manufacturer claims that only 10% of all new drugs that are shown to be effective in animal tests ever pass through all the additional testing required to be marketed. The manufacturer currently has eight new drugs that have been shown to be effective in animal tests, and they await further testing and approval. You are not allowed to use PHStat4 for this question. Show your calculations clearly by labeling them properly so that it is clear to infer what the calculations are for

a. Find the probability that none of the drugs is marketed.

b. Find the probability that at least 2 are marketed.

c. Find the expected number of marketed drugs among the eight.

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********I NEED THE BELL SHAPED CURVE, PLEASE DON'T ANSWER IF YOU CAN'T INCLUDE***********

********I NEED THE BELL SHAPED CURVE, PLEASE DON'T ANSWER IF YOU CAN'T INCLUDE***********

According to the Organization for Economic Co-Operation and Development (OECD), adults in the United States worked an average of 1,805 hours in 2007. Assume the population standard deviation is 395 hours and that a random sample of 70 U.S. adults was selected. a. Calculate the standard error of the mean. b. What is the probability that the sample mean will be more than 1,775 hours? c. What is the probability that the sample mean will be between 1,765 and 1,820 hours? d. Would a sample mean of 1,815 hours support the claim made by the OECD? Explain?