A growing concern of employers is time spent in activities like surfing the Internet and e-mailing friends during work hours. The San Luis Obispo Tribune summarized the fundings from a survey of a large sample of workers in an article that ran under the headline "Who Goofs Off 2 Hours a Day? Most Workers, Survey Says" (August 3, 2006). Suppose that the CEO of a large company wants to determine whether the average amount of waisted time during an 8-hour work day for employees of her company is less than the reported 120 minutes. Each person in a random sample of 12 employees was contacted and asked about daily waisted time at work. The resulting data are the following:

108   112 117 128 130 111 131 116 113 113 105    128

The CEO wants to determine if these data provide evidence that the mean wasted time for this company is less than 120 minutes. Assuming that the population distribution is approximately normal, find the P-value for this test.

Make the following:

a. frequency distribution

b. pareto chart

c. probability distribution

d. pie graph

for the following set of numbers :

Prophecy - 15 out of 50

Advice - 7 out of 50

Wisdom - 17 out of 50

Compliments - 4 out of 50

Misc. - 7 out of 50

Regression analysis consists of two major tasks: (i) estimation of population parameters and (ii) hypothesis testing (e.g., t-test, F-test) or the application of inferential statistics to the estimated parameters. We learned OLS (ordinary least square) principle as the major estimation tool (thereby fulfilling the first task). There is a critically important assumption that we have to make in order to perform the second task (that is, to conduct hypothesis testing with respect to estimated parameters). Identify and discuss it. (10 points)

A study of fox rabies in a country gave the following information about different regions and the occurrence of rabies in each region. A random sample of

n₁ = 16

locations in region I gave the following information about the number of cases of fox rabies near that location.

x₁:

   Region I Data

A second random sample of

n₂ = 15

locations in region II gave the following information about the number of cases of fox rabies near that location.

x₂:

   Region II Data

(i) Use a calculator with sample mean and sample standard deviation keys to calculate x₁ and s₁ in region I, and x₂ and s₂ in region II. (Round your answers to two decimal places.)

(ii) Does this information indicate that there is a difference (either way) in the mean number of cases of fox rabies between the two regions? Use a 5% level of significance. (Assume the distribution of rabies cases in both regions is mound-shaped and approximately normal.)
(a) What is the level of significance?

PROBLEM:

The average hourly wage of carpenters is normally distributed with a population mean of $62.00 and a population standard deviation of $8.00. Calculate the following:

(a) The proportion of carpenters earning between $48 and $50.

(b) The proportion of carpenters earning more than $67.

(c)The proportion of carpenters earning less than $52.

(d) The 85^th percentile.

What is the equipment variation as a percent of process variation using ANOVA

Part   Appraiser   Trial   Measurement
1   1   1   12.369
1   1   2   11.957
1   2   1   12.915
1   2   2   13.065
1   3   1   13.894
1   3   2   13.86
1   4   1   15.055
1   4   2   15.081
2   1   1   18.26
2   1   2   18.271
2   2   1   19.068
2   2   2   19.089
2   3   1   20.197
2   3   2   20.176
2   4   1   20.665
2   4   2   20.553
3   1   1   19.607
3   1   2   19.749
3   2   1   20.478
3   2   2   20.374
3   3   1   20.402
3   3   2   20.454
3   4   1   22.133
3   4   2   22.405
4   1   1   26.056
4   1   2   25.813
4   2   1   26.895
4   2   2   26.921
4   3   1   28.991
4   3   2   28.981
4   4   1   30.695
4   4   2   30.872
5   1   1   28.498
5   1   2   28.723
5   2   1   31.671
5   2   2   31.678
5   3   1   33.357
5   3   2   33.385
5   4   1   34.607
5   4   2   34.511
6   1   1   37.184
6   1   2   37.029
6   2   1   37.806
6   2   2   37.809
6   3   1   38.379
6   3   2   38.493
6   4   1   39.25
6   4   2   38.848

Find and sketch the critical value(s) and the rejection region for a left-tailed t-test with α =0.02 and n=42.

Directions: Solve the following problems, detailing and documenting the solutions. Additional instructions: For each problem, be sure to include the (a) type of parametric or nonparametric testing being performed; (b) both null and research hypotheses; (c) critical value and test statistic; (d) p-value; and (e) both technical and contextual conclusions. 1. The back offices for the five department stores that anchor Pinelands Promenade Mall dispute whether or not they receive comparable treatment by mall management. In response, mall management hired a consulting firm to investigate whether or not customer preferences among shoppers for these five department stores are comparable or equivalent. Research assistants collected a random sample of 240 people at the mall, asking these mall visitors which department store they preferred most. The resulting frequency data was as follows: Onyx Paisley’s Quarterdeck Regal Sale-Mart 54 60 36 48 42 What should the consulting firm report to mall management? In other words, according to the available evidence, and testing at the 5% level of significance, is the proportion of mall visitors who prefer each of the five department stores at Pinelands Promenade the same? [COMMENTS & HINTS: It is good to see how the data fits the claim.]

Computers Magazine has recently completed an analysis of its customer base. It has determined that 75% of the issues sold each month are subscriptions and the other 25% are sold at newsstands. It has also determined that the ages of its subscribers are normally distributed with a mean of 44.5 and a standard deviation of 7.42 years, whereas the ages of its newsstand customers are normally distributed with a mean of 36.1 and a standard deviation of 8.20 years.

(a) Computers Magazine would like to make the following statement to its advertisers: “80% of our subscribers are between the ages of . . . and . . . .” Your job is to fill in the blanks, choosing a range that is symmetric around the mean. (In other words, the mean age of subscribers should be the midpoint of the range.)

(b) What proportion of Computers Magazine newsstand customers have ages in the range you gave in (a)?

(c) What proportion of all of Computers Magazine customers have ages in the range you gave in (a)?

RESUBMITTING AS PREVIOUS SUBMISSION BY ANONYMOUS WAS INCORRECT

The accompanying table contains the service ratings of 14 different Internet and TV providers. Level of significance is .10. Complete parts​ (a) through​ (d) below

Determine the T Test

Determine the P value

Construct and interpret a 90​% confidence interval estimate of the difference in the mean service rating between TV and Internet services

1. A sports psychologist gave a questionnaire about healthy eating habits to randomly selected professional athletes. The results are displayed below. Using the .05 significance level, is there a difference in healthy eating habits among professionals in the three sports?

                       Baseball Players              Basketball Players              Football Players

                                        32                                           27                                           16

                                        27                                           36                                           13

                                        26                                           25                                           15

                                        35                                           30                                           10

Step 1: State Hypotheses (2 points)

• Null:

• Research:

Step 2: Determine Comparison Distribution (1 point)

• What is the distribution shape and degrees of freedom for the comparison distribution?

Step 3: Set the Criteria for a Decision (3 points)

• df_B =

df_W=

• Critical value:

Step 3: Compute the Test Statistic (10 points)

Step 5: Make a Decision (9 points)

Reject/Fail to Reject the null?

If necessary, compute a Tukey’s HSD post hoc test.

Write your results as they would appear in a research journal (~two sentences).

The correct degrees of freedom for a dependent samples t­test with 55 participants in each group would be equal to ________.

You are at a wetland site. You have been instructed to test for chromium contamination. Suppose that a regulatory agency has determined that a population mean chromium concentration equal to 7 mg/kg characterizes the no-contamination state. Likewise, a population mean chromium concentration significantly greater than 7 mg/kg characterizes the contamination state. Suppose that 12 soil tests were conducted around different areas around the wetland site. Their chromium concentration analyzed with the following results. Use this information for the 9 problems. Do not round.

6.223 6.995 10.333 7.265 7.833 7.111 6.986 8.934 9.167 7.505 7.301 7.213

1. Describe the population of interest and hypothesized parameter for this scenario.

2. Find the mean of the sample. Use the formula and show the steps for finding the sample mean.

3. Find the median of the sample. Use the formula and show the steps for finding the sample median.

4. Find the standard deviation of the sample. Use the formula and show the steps.

5. Using the appropriate symbols, write the hypotheses.

6. Calculate the test statistic showing the work with the formula.

7. Using StatCrunch, determine the p-value for the hypothesis test using the appropriate probability distribution (do not just use the t test for a single mean output).

8. Make the decision for the test in terms of the null hypothesis. Explain how you arrive at this decision.

9. Write the conclusion with minimal statistical jargon and answer the research question of interest as demonstrated in the presentations.

We work for Cola Company and there have been some discussions on which pressure setting is best for filling out bottles. If we overfill the bottles then we are spending money we do not need to. If we are under filling the bottles we run the risk of dissatisfaction of the customers. If we can fill the bottles using a higher psi we can run the line faster and thus increase our production. Our current fill pressure is 25psi. Management wants to know if there is a different variation from the standard between the two pressure settings.

ml (25psi volume): 1007.2, 1008.4, 1010.2, 1011.2, 1008.0, 1009.0, 1011.4, 1013.4, 1010.6, 1010.9

ml (30psi volume): 1001.2, 1003.1, 1003.6, 1001.4, 1002.7, 1004.3, 1002.6, 1005.0, 1003.7, 1004.4

Sample size of first set =

Sample size of second set =

Sample mean of first set =

Sample mean of second set =

Sample standard deviation of the first set =

Sample standard deviation of the second set =

Estimate of variance =

Confidence Coefficient =

Alpha =

Calculated Degrees of Freedom =

Calculated Test Statistic =

What can you conclude by observing your confidence limits? (No difference or there is a difference?) =

Consider the following data: 43 54 55 63 67 68 69 77 85 Suppose that the last value is actually 115 instead of 85. What effect would this new maximum have on the median of the data?

increase the value of the median

decrease the value of the median

no effect

1. Approximately, what z-score divides the lower 75% of the data from the upper 25%?

   1. z = 0.75

   2.   z = 0.675

   3.   z = - 0.675

   4.   z = -0.25

   5.   none of the above