A clinical trial is conducted comparing a new (investigational) analgesic drug to one already on the market (Tylenol) for arthritis pain. Participants were randomly assigned to only one of the two treatment groups and the outcome was self-reported pain relief within 30 minutes. The 2 x 2 crosstab analysis with SPSS produced the following results: Chi-Square Tests Value df Asymp. Sig. (2-sided) Exact Sig. (2-sided) Exact Sig. (1-sided) Pearson Chi-Square 11.161a 1 .001 Continuity Correctionb 10.212 1 .001 Likelihood Ratio 11.349 1 .001 Fisher's Exact Test .001 .001 Linear-by-Linear Association 11.115 1 .001 N of Valid Cases 240 a. 0 cells (0.0%) have expected count less than 5. The minimum expected count is 32.50. b. Computed only for a 2x2 table Note: Footnote “a” is very important because it tells us about a potential violation of a Pearson chi-square test assumption. 25. Is there a violation of the Pearson chi-square test assumption?

Q2. Proportions (percentages) in a Z Distribution

A large population of scores from a standardized test are normally distributed with a population mean (μ) of 50 and a standard deviation (σ) of 5. Because the scores are normally distributed, the whole population can be converted into a Z distribution. Because the Z distribution has symmetrical bell shape with known properties, it’s possible to mathematically figure out the percentage of scores within any specified area in the distribution. The Z table provides the percentages corresponding to any Z score.

a. John has a score of 55. What is John’s Z score?

b. What is the percentage of students that score lower than John?

c. Based on the Z table, if 1000 students take the test, how many of them would likely score above John’s score? (Round the answer to a whole number)

d. Tom has a score of 40. What is Tom’s Z score?

e. What is the percentage of students that score lower than Tom?

f. What is the percentage of students that score between John and Tom?

g. Based on the Z table, if 1000 students take the test, how many of them would likely score below Tom’s score?

h. Anna scores at the 99^th percentile on this exam, what is her Z score?

Hint: A score at 99^th percentile means 99% of the scores are below this score.

i. Based on the result of the previous question, what is Anna’s actual score on the exam?

j. What would be the median score on this exam?

Hint: Review the definition of “median” and then figure out the percentage of scores below (or above) this score.

1) One out of every 92 tax returns that a tax auditor examines requires an audit. If 50 returns are selected at random, what is the probability that less than 3 will need an audit? 0.0151 0.9978 0.0109 0.9828

2) Sixty-seven percent of adults have looked at their credit score in the past six months. If you select 31 customers, what is the probability that at least 20 of them have looked at their score in the past six months? 0.142 0.550 0.692 0.450

3) Ten rugby balls are randomly selected from the production line to see if their shape is correct. Over time, the company has found that 89.4% of all their rugby balls have the correct shape. If exactly 6 of the 10 have the right shape, should the company stop the production line? No, as the probability of six having the correct shape is not unusual Yes, as the probability of six having the correct shape is not unusual No, as the probability of six having the correct shape is unusual Yes, as the probability of six having the correct shape is unusual

What are the two main advantages of factorial experiments?

This question from statistics.

Management of a soft-drink bottling company wants to develop a method for allocating delivery costs to customers. Although one cost clearly relates to travel times within a particular route, another variable cost reflects the time required to unload the cases of soft drink at the delivery point. A sample of 20 deliveries within a territory was selected. The delivery time and the number of cases delivered were recorded. Develop a regression model to predict delivery time based on the number of cases delivered. a) Use the least-square method to calculate the regression coefficients, b0 and b1. Write your regression equation. b) Interpret the meaning of b0 and b1 in this problem. c) Predict the delivery time for 150 cases of soft drink. d) Would it be appropriate to use to model to predict the delivery time for a customer who is receiving 500 cases of soft drink? Explain why. e) Determine the coefficient of determination, r2, and explain it meaning in this problem. f) Perform a residual analysis. Is there any evidence of patterns in the residuals? Explain. g) At the 0.05 level of significance, is there evidence of a linear relationship between delivery time and the number of cases delivered? Explain. h) Explain how the results in a to g can help allocate delivery costs to customers.

You roll two fair dice. Let A be the event that the sum of the dice is an even number. Let B be the event that the two results are different.

(a) Given B has occurred, what is the probability A has also occurred?

(b) Given A has occurred, what is the probability B has also occurred?

(c) What is the probability of getting a sum of 9?

(d) Given that the sum of the pair of dice is 9 or larger, find the probability that the sum of the pair of dice is exactly 10.

Some people say if you want to make money after you graduate that you should major in something \technical." A survey of 1400 recent graduates showed that students who had taken two or more classes in statistics had an average salary of $42,571 (n = 428, s = 5600) while those who hadn't taken as many statistics courses had an average salary of $38,200 (n = 972, s = 6000). Is the conventional wisdom true; should students that want to earn more consider taking statistics?

Tom Sevits is the owner of the Appliance Patch. Recently Tom observed a difference in the dollar value of sales between the men and women he employs as sales associates. A sample of 40 days revealed the men sold a mean of $1,400 worth of appliances per day. For a sample of 50 days, the women sold a mean of $1,500 worth of appliances per day. Assume the sample standard deviation for men is $200 and for women $250. At the 0.05 significance level, can Mr. Sevits conclude that the mean amount sold per day is larger for the women? (Assume unequal variances. Report t test statistic, critical values in 4 decimals)

The steps for testing whether the population mean sales for women is greater than the population mean sales for men is listed below for a significance level of 0.05. Fill in the blanks.

Determine the rejection rule,

What is the numerator value for the test statistic, i.e. when you are calculating the test statistic, what value do you get for the numerator?_________

What is the denominator value for the test statistic? __________

Test statistic value :____________ (4 decimals)

Studies have shown that the frequency with which shoppers browse Internet retailers is related to the frequency with which they actually purchase products and/or services online. The following data show respondents age and answer to the question “How many minutes do you browse online retailers per week?”

Age Time

13 5662

19 4549

16 3772

44 1872  

32 2799

52 1355

39 1966

15   5682

40 1602

53 1186

48 1832

37 2253

36 2241

42 1001

30 2474

42 1943

28 3021

11 5682

32 2192

39 1784

23 2707

37 1801

17 4827

11 2693

18 4340

50 1399

52 1593

9 9154

41 1504

26 2627

30 2575

32 2711

53 2368

1. Use Data > Data Analysis > Correlation to compute the correlation checking the Labels checkbox.

2. Use the Excel function =CORREL to compute the correlation. If answers for #1 and 2 do not agree, there is an error.

3. The strength of the correlation motivates further examination. a) Insert Scatter (X, Y) plot linked to the data on this sheet with Age on the horizontal (X) axis. b) Add to your chart: the chart name, vertical axis label, and horizontal axis label. c) Complete the chart by adding Trendline and checking boxes

4. Read directly from the chart a) Intercept = b) Slope = c) R2 = Perform Data > Data Analysis > Regression.

5. Highlight the Y-intercept with yellow. Highlight the X variable in blue. Highlight the total standard error in orange SUMMARY OUTPUT

6.Use Excel to predict the number of minutes spent by a 37-year old shopper. Enter = followed by the regression formula. Enter the intercept and slope into the formula by clicking on the cells in the regression output with the results.

7. Is it appropriate to use this data to predict the amount of time that a 68-year-old will be on the Internet? If yes, what is the amount of time, if no, why?

The following table is used for a number of questions below. The table above shows the responses of a survey of teenagers aged 14-18 when asked at what age they thought they would become financially independent.

1. What do the teens expect is the probability of being financially independent before age 25?
2. A recent Gallup poll found that only 14 percent of 24- to 34-year-olds are financially independent. Do teens have realistic expectations?

Problem # 9: Family income 2011 According to Statistics Canada, Income Statistics Division, the mean after-tax family income in 2011 was $63000, while the median was $50700. In contrast to 2011 dollars, the mean and median in 1980 were $50000 and $49500 respectively. 1. Why did you expect to find a higher mean than median in both years? Draw a very rough plot of what the histogram for 2011 incomes might look like. 2. How much higher was the mean compared with the median in 2011, in percentage terms? How much higher in 1980? What does this suggest about how the income distribution has changed in Canada? Draw two very rough histograms to represent what the two distributions might look like in comparison to each other. Are the rich getting richer, and the poor poorer? Explain your answer. 3. Suppose that in 2030, the mean and median in actual 2030 dollars are $80000 and $60000 respectively. Have the rich gotten richer, and the poor poorer? Say what you can about what appears to be going on with incomes, based on this limited information.

Use Excel to perform various analyses and generate graphs, charts and plots of the following activities: generate frequency tables; produce bar graphs, pie charts, line charts, and scatter plots; calculate mean, median, and mode, standard deviation, standard scores, and normal distribution percentiles.

Finish times (to the nearest hour) for 10 dogsled teams are shown below.

Make a frequency table showing class limits, class boundaries, midpoints, frequency, relative frequencies, and cumulative frequencies. Use three classes.

(Round your answer for relative frequency to one decimal place and for midpoint to the nearest whole number.) 283 265 236 310 275 301 287 258 299 280

Write out a chart or explain in writing how you would conduct an experiment on retroactive interference. Make sure to clearly indicate what is given to both the control and experimental groups. (6 Points)

Find the best regression equation that gives selling price as a function of living area, taxes, acreage and rooms.