The concession stand at the Shelby High School stadium sells slices of pizza during soccer games. Concession stand sales are a primary source of revenue for high school athletic programs, so the athletic director wants to sell as much food as possible. However, any pizza not sold is given away to the players, coaches, and referees, or it is thrown away. The athletic director wants to determine a reorder point that will meet, not exceed, the demand for pizza. Pizza sales are normally distributed, with a mean of 6 pizzas per hour and a standard deviation of 2.5 pizzas. The pizzas are ordered from Pizza Town restaurant, and the mean delivery time is 30 minutes, with a standard deviation of 8 minutes.

1. Currently, the concession stand places an order when it has 1 pizza left. What level of service does this result in?
2. What should the reorder point be to have a 98% service level?

You are part of a marketing team that needs to research the potential of a new product. Your team decides to e-mail an interactive survey to a random sample of consumers. Write a short questionnaire that will generate the information you need about the new product. Select a sample of 200 using an SRS from your sampling frame. Discuss how you will collect the data and how the responses will help your market research.

5. (18 pts) Consider the following situation, and answer each of the following multiple-choice questions. Indicate your answer next to each question in the blank. Possible answers are: A = it increases; B = it decreases; C = it stays the same; D = not enough information to say for sure. No need to restate the question or to justify your answer.

______A. As sample size decreases, what happens to the standard error?   

______B. As a sample becomes less and less representative of the population from which it is drawn, what happens to the value of the sample mean?

______C. As |zobt| increases, what happens to the p value?

______D. As |zobt| increases, what happens to alpha?

______E. As power increases, what happens to the probability of correctly rejecting the null hypothesis?

______F. As N increases, what happens to |zcrit|?

______G. As N increases, what happens to |zobt|?

______H. As the number of tails increases from one to two, what happens to |zcrit|?

______I. As the absolute value of the difference between means decreases, what happens to the absolute value of Cohen’s d?

______J. If the standard error decreases in value only because the sample size changed, what will happen to the absolute value of Cohen’s d?

______K. As N increases, what happens to |tobt|? (Assume the increase in N does not affect the value of s.)  

______L. As degrees of freedom increase, what happens to |tcrit|?

______M. As degrees of freedom increase and alpha decreases in value, what happens to |tcrit|?

______N. As the difference between means increases and the sample standard deviation decreases, what happens to |tobt|?

______O. As degrees of freedom decrease in a single sample t test, what happens to power?

______P. As |tobt| decreases, what happens to |tcrit|?

______Q. As |robt| increases, what happens to the likelihood of rejecting the H0 that ρ = 0?

______R. As N decreases and alpha decreases in value, what happens to |rcrit|?

show that standardized poisson follows poisson with mean 0 and variance 1

Conestoga college recently released a flyer in an attempt to recruit accounting students for their business school. In the flyer, Conestoga college claims that the mean first year graduate salary of their accounting students is $50,000, whereas their biggest competition for accounting students, Fanshawe College, have a first year graduate salary of only $45,000.

After reading Conestoga's recruiting flyer, Fanshawe College executives believe that Conestoga falsely stated the graduate salaries and as a result have conducted their own study. Based on the sample below, at 1% level of significance is there evidence that Conestoga's first year accounting graduates salaries are less than claimed?

BLANK #1: Is this a question involving mean or proportion? ***ANSWER "MEAN" OR "PROPORTION" (WITHOUT THE QUOTATION MARKS)***

BLANK #2: Which type of distribution should be used to calculate the probability for this question? ***ANSWER "NORMAL", "T", OR "BINOMIAL" (WITHOUT THE QUOTATION MARKS)***

BLANK #3: Which of the following options are the appropriate hypotheses for this question: ***ANSWER WITH THE CORRECT LETTER, WITHOUT ANY QUOTATION MARKS OR BRACKETS***

A) H₀: μ = $50,000 H₁: μ > $50,000

B) H₀: μ = $50,000 H₁: μ < $50,000

C) H₀: μ = $50,000 H₁: μ ≠ $50,000

D) H₀: p = $50,000 H₁: p > $50,000

E) H₀: p = $50,000 H₁: p < $50,000

F) H₀: p = $50,000 H₁: p ≠ $50,000

BLANK #4: What is the p-value of this sample? ***ANSWER TO 4 DECIMALS, BE SURE TO INCLUDE LEADING ZERO, EXAMPLE "0.1234"...NOT ".1234"***

BLANK#5: Based on this sample, at 1% level of significance is there evidence that Conestoga's first year accounting graduates salaries are less than claimed? ***ANSWER "YES" OR "NO" (WITHOUT THE QUOTATION MARKS)***

In what follows use any of the following tests/procedures: Regression, confidence intervals, one-sided t-test, or two-sided t-test. All the procedures should be done with 5% P-value or 95% confidence interval.

Use the Weight_vs_IQ data. SETUP: Common sense dictates that a person’s IQ and Weight should not be related. However, one never knows until one examines the data. Given the data (IQ and weight for 29 students) your job is to check if the common sense assumption is reasonable or maybe it is not.

13. What test/procedure did you perform?

• a. One-sided t-test
• b. Two-sided t-test
• c. Regression
• d. Confidence interval

14. What is the P-value/margin of error?

• a. 0.749971
• b. 8.2E-06
• c. 0.711936
• d. 0.355968

15. Statistical interpretation

• a. Since the P-value is very small, we can confirm the common sense assumption that IQ and Weight are not related.
• b. Since the P-value is large, we cannot claim that averages are different.
• c. Since the P-value is large, we cannot claim that IQ and Weight are related.
• d. None of these.

16. Conclusion

• a. I have no statistical evidence to claim that IQ and Weight are related.
• b. I am confident that IQ and Weight are related.
• c. I am confident that IQ and Weight are not related.

DATA:

Weight  IQ
88      99
112     103
107     97
112     99
80      100
86      90
103     118
121     79
116     80
82      88
65      82
107     103
100     116
91      112
110     92
113     115
105     100
108     94
90      118
73      106
102     126
99      95
80      119
114     116
90      79
95      92
106     78
86      111
106     80

Table below shows monthly beer sales at Gordon’s Liquor Store in 2017.

The sales manager had predicted that January 2017 beer sales would be 950.

• Forecast beer sales needed for January 2018 using the moving average with 3 periods.

• Forecast beer sales needed for January 2018 using an exponential smoothing method with α = 0.2 and α = 0.9

• What is the best method to forecast the beer sales according to MSE. (moving average with 3 periods, exponential smoothing method with α = 0.2, or exponential smoothing method with α = 0.9)

Data on pull-off force (pounds) for connectors used in an automobile engine application are as follows: 79.7 75.1 78.2 74.1 73.9 75.0 77.6 77.3 73.8 74.6 75.5 74.0 74.7 75.9 72.5 73.8 74.2 78.1 75.4 76.3 75.3 76.2 74.9 78.0 75.1 76.8 If necessary, round all intermediate calculations to four decimal places (e.g. 12.3456). (a) Calculate a point estimate of the mean pull-off force of all connectors in the population (Round the answer to four decimal places (e.g. 90.2353).) (b) Calculate a point estimate of the pull-off force value that separates the weakest 50% of the connectors in the population from the strongest 50% (Express the answer to two decimal place (e.g. 90.15).) (c) Calculate the point estimate of the population variance (Round the answer to three decimal places (e.g. 3.567).) (d) Calculate the point estimate of the population standard deviation (Round the answer to two decimal places (e.g. 1.23).) (e) Calculate the standard error of the point estimate found in part (a) (Round the answer to two decimal places (e.g. 1.23).) (f) Calculate a point estimate of the proportion of all connectors in the population whose pull-off force is less than 73 pounds (Round the answer to three decimal places (e.g. 0.123).)

Left ventricular mass (LVM) is an important risk factor for subsequent cardiovascular disease. A study is proposed to assess the relationship between childhood blood pressure levels and LVM in children as determined from echocardiograms. The goal is to stratify children into a normal bp group (< 80th percentile for their age, gender, and height) and an elevated bp group (≥ 90th percentile for their age, gender, and height) and compare change in LVM between the 2 groups. Before this can be done, one needs to demonstrate that LVM actually changes in children over a 4-year period.

To help plan the main study, a pilot study is conducted where echocardiograms are obtained from 10 random children from the Bogalusa Heart Study at baseline and after 4 years of follow-up.

Implement an appropriate 2-sided test to test the hypothesis that there is a change in mean LVM over 4 years?

You must clearly write out all 4 steps of the appropriate hypothesis test clearly defining the parameter(s) involved, calculate the value of the test statistic and the p-value, and state your conclusion in the context of the problem.

Considering the following observations for an amount of polymerization of a certain specimen:

418 421 421 422 425 427 431 434 437 439 446 447 448 453 454 463 465

a) Using Minitab, construct and interpret a boxplot.

b) Is it plausible that the given sample observations were selected from a normal distribution?

c) Calculate a two-sided 95% confidence interval for true average amount of polymerization. Does the

interval suggest that 440 is a plausible value for true average? What about 450? (Use Minitab when

necessary)

A journal article reports that 34% of fathers take no responsibility for child care. A group of fathers believes that this estimate is too high. In a random sample of 80 fathers, it was found that 23 of those father take no responsibility for child care. Is there significant evidence at the 1% significance level that less than 34% of father take no responsibility for child care?

The following data show weight (in kg) of 24 women in a study: 46.4, 53.2, 52.8, 42.0, 50.8, 43.0, 51.9, 59.2, 55.1, 38.9, 49.7, 49.9, 43.1,42.2, 52.7, 49.8, 50.7, 44.8, 49.2, 47.7, 42.9, 52.9, 54.1, 45.4. Prepare the following:

I. A frequency distribution,

II. A relative frequency distribution,

III. A cumulative frequency distribution,

IV. A cumulative relative frequency distribution,

V. A stem-and-leaf plot, and

VI. Comment on the findings.

Using Rcode solve

A company with a large fleet of cars wants to study the gasoline usage. They check the gasoline usage for 50 company trips chosen at random, finding a mean of 25.02 mpg and sample standard deviation is 4.83 mpg.

a. Which kind of confidence interval is appropriate to use here, z-interval or t-interval?

b. What are the assumptions to check for the interval you chose?

c. Please use R to find the critical value the company needs when constructing a (two-sided) 98% CI.

d. Please use R to construct a (two-sided) 98% CI for the mean of the general gasoline usage.

e. Please use R to construct a 98% upper confidence bound for the mean of the general gasoline usage.

f. Create a R function whose argument is the width of CI, and the output is the sample size necessary to achieve such accuracy. The confidence level is fixed at 98%.

g. Apply the function you created in part (f) to demonstrate that larger sample size is required to achieve better accuracy (i.e, narrower CI width). Confidence level is fixed at 98%. Show at least three examples

A furniture store has maintained monthly sales records for the past 20​ months, with the results shown below.

Assume you have determined there is NO SEASONALITY in this time series.​ Therefore, you want to fit a linear trend model​ (that is, trend​ only) to the data.

Calculate the linear trend equation.​ (Round coefficients to the nearest whole​ number.)

y Subscript t Baseline equalsyt=nothing​+

nothing​*t

What are the test statistic and​ p-value to test for a significant trend. Round both to two decimal places.

T​ = nothing

​p-value = nothing

Is the trend significant using a​ 10% significance​ level?

Yes

No

What is the value of​ R-squared? (Round to two​ decimals.)

nothing

Forecast the sales for the next month​ (t =​ 21). (Round to the nearest whole​ number.)

Upper F 21 equalsF21=nothing

Based on the​ R-squared value, how confident are you in this​ forecast? (That​ is, how accurate do you think the forecasts will​ be?)

A.

Not confident at all because the​ R-squared value is so low

B.

Very confident because the​ R-squared value is high

C.

Somewhat confident because the​ R-squared value is moderate​ (not extremely high but not extemely​ low)