1. The data in fit4fun.xls contain 108 rows of data. The X column is represented by column M "Amount spent on Meal Plan" and Y column is represented by column O " Total Spent".
   Consider the 108 rows of data as a population : find the mean and standard deviation for the Y-column of "Total Spent":
   = __________, = __________
2. Please use ‘randbetween’ to select 20 different random numbers (no 2 are the same) between 1 and 108. Use these as index numbers to select your 20 rows for your sample. This is selecting a random sample of 20 without replacement. Note: the X column is again the "Amount spent on Meal Plan" and the Y column is "Total Spent " . For this sample of 20 points, find the mean and standard deviation. (you should have already done this earlier and you may provide a spread sheet here instead)

My Random Numbers My Random Sample of Y values

The mean for this sample is:__ __ (Y Value)

The standard deviation for this sample is:____ (Y Value)

1. Find the 90% confidence interval for the population mean using this sample data of 20 data points found in question 2.

1. You may assume knowledge of the population standard deviation from question 1 and that the population is approximately normal. Discuss your result in context of your knowledge of the population (that is the average of the Total spent and YOU KNOW the population mean and standard deviation from problem 1.) That is, does the sample data reflect accurately that of the population in your case? If so, is it what you expected? If not, give an explanation of why not.
   Explanation:
2. Repeat, this time you may not assume knowledge of the population standard deviation. (i.e.You do not know the values from problem 1.)

Explanation:

2. You are trying to test the claim that the mean amount spent in total by the clients of fit4fun is more than $2500. Test this claim using your 20 point sample. Test at the α = .05 significance level.

Remark: Follow the steps for hypothesis testing given in the text.

1. Using the sample of 20 data points you have, test at the = .05 significance level. You may assume that you know what the population standard deviation is from question 1 and that it is approximately normally distributed. Discuss the result of your test in context of what you already know to be true (from problem 1.)

Hypothesis Steps

1. State Null Hypothesis –
2. State Alternative Hypothesis –
3. Choose Alpha
4. What is n ?
5. Choose Test – Z test or T test – Z test (sigma known) and give critical value(s):
6. Collect Data –
7. Compute Test Statistic –
8. Make Statistical Decision –
9. Explain your decision –

1. Repeat, this time you may not assume knowledge of the population standard deviation. (Assume you do not have the results from problem 1.)

3. For your 20 point sample with X value representing "Amount spent on Meal Plan" and Y value representing "Total spent":

1. Use Excel to provide a scatter diagram below and determine if the data looks as if it is appropriate for regression analysis.
   Use Excel to do a residual plot. From observing the residual plot, do you think the following conditions for regression are satisfied?
   Is the data linear? _____ _ If not what would you do?___________________
   Is the Normality condition satisfied?____ __________ Explain___ ____________
   Is the Homoscadascity condition satisfied?___ ______ Explain_____ _________
   Do we have independence of errors? __ _ __ Explain_____ _ _______________
   (No explanation, no credit)
2. Assuming that the conditions for regression analysis are all satisfied, perform the regression analysis using Excel and provide the printout below:
3. State the regression equation
   
4. Using the printout, test the hypothesis that there is not a linear relationship between "Amount spent on Meal Plan" and "Total Spent" at the alpha = .05 significance level. Please give the t-statistic and the p-value of your test.
5. Predict the "Total Spent", if the client is spending $3000 for his/her "Amount spent on Meal Plan"
6. Suppose: The following are 2 confidence intervals for predicting the "Total Amount Spent" for "Amount spent on Meal Plan" of $3000
   (3724.72, 3870.79) and (3167.52, 4427.51)
   What is the point estimate?_ _
   Circle the interval above that is for average predicted Y value.
   (The other one is for Individual Response Y. You do not have to confirm where these numbers come from. )
7. Given the information from above.
8. (i). Discuss whether the Amount spent on Meal Plan is a good predictor of the Total Amount spent by clients of fit4fun (Give the coefficient of determination.)

(ii). Do you think Susie Thompson should continue in this business or not. Explain! You should assume that the 108 files you have are just a large sample. She has several thousands of clients in total.

(iii). What sort of study do you advise her to do next?

Price: $27.25

Solution: The downloadable solution consists of 14 pages, 1325 words and 4 charts.
Deliverable: Word Document