Use RStudio. To test if a middle school class on geography is working, a pre- and post-test were given to students at the start and end of the semester. Assume that the scores were randomly selected from the two tests. Also, assume that that they are pairs of scores for ten students. Use the following data to test if the class improved students’ knowledge of geography. (hint: use “var.equal=TRUE” in your argument)

Scores

Pre-test:     77, 56, 64, 60, 57, 53, 72, 62, 65, 66

Post-test: 88, 74, 83, 68, 58, 50, 76, 64, 74, 60

The mean throwing distance of a football for a Luis, a high school freshman quarterback, is 50 yards, with a standard deviation of three yards. The team coach tells Luis to adjust his grip to get more distance. The coach records the distances for 35 throws. For the 35 throws, Luis’s mean distance was 54 yards. The coach thought the different grip helped Luis throw farther than 50 yards. Conduct a hypothesis test using a preset α = 0.01. Assume the throw distances for footballs are normal.

a. Determine what type of test this is: A, B or C? A) Single population mean with standard deviation known B) Single population mean with standard deviation not known C) Single population proportion

b. Identify the null hypothesis, A, B,C or D? Identify the alternative hypothesis, A, B,C or D ? A) mu greater or equal than 50 B) mu greater than 50 C) mu less or equal than 50 D) mu less than 50

c. Find the p-value to nearest whole number

d. State your conclusion, A, B, or C? A. Can't reject null. There is not sufficient evidence from this sample data to show that Luis’s mean throwing distance is greater than 50 yards. B. Reject null. There is sufficient evidence from this sample data to show that Luis’s mean throwing distance is greater than 50 yards. C. no conclusion

Salaries for teachers in a particular elementary school district are normally distributed with a mean of $41,000 and a standard deviation of $6,100. We randomly survey ten teachers from that district.

A. Give the distribution of ΣX. (Round your answers to two decimal places.)

ΣX - N ( , )

B. Find the probability that the teachers earn a total of over $400,000. (Round your answer to four decimal places.)

C. Find the 80^th percentile for an individual teacher's salary. (Round your answer to the nearest whole number.)

D. Find the 80^th percentile for the sum of ten teachers' salary. (Round your answer to the nearest whole number.)

At the beginning of the school year, Craig Kovar decided to prepare a cash budget for the months of September, October, November, and December. The budget must plan for enough cash on December 31 to pay the spring semester tuition, which is the same as the fall tuition. The following information relates to the budget:

a. Prepare a cash budget for September, October, November, and December. Use the minus sign to indicate cash outflows, a decrease in cash or cash payments.

b. Are the four monthly budgets that are presented prepared as static budgets or flexible budgets?

c. What are the budget implications for Craig Kovar?

Craig can see that his present plan   sufficient cash. If Craig did not budget but went ahead with the original plan, he would be $fill in the blank 918bcdf8d05207b_3   at the end of December, with no time left to adjust.

1. At the beginning of the school year, Craig Kovar decided to prepare a cash budget for the months of September, October, November, and December. The budget must plan for enough cash on December 31 to pay the spring semester tuition, which is the same as the fall tuition. The following information relates to the budget:

   Cash balance, September 1 (from a summer job)	$10,850
   Purchase season football tickets in September	200
   Additional entertainment for each month	310
   Pay fall semester tuition in September	5,600
   Pay rent at the beginning of each month	750
   Pay for food each month	690
   Pay apartment deposit on September 2 (to be returned December 15)	750
   Part-time job earnings each month (net of taxes)	1,500

   This information has been collected in the Microsoft Excel Online file. Open the spreadsheet, perform the required analysis, and input your answers in the questions below.

   Open spreadsheet

   a. Prepare a cash budget for September, October, November, and December. Enter all amounts as positive values except cash decrease which should be indicated with a minus sign.

   Craig Kovar
   Cash Budget
   For the Four Months Ending December 31
   	September		October		November		December
   Estimated cash receipts from:
   		$		$		$		$
   Total cash receipts		$		$		$		$
   Less estimated cash payments for:
   		$
   				$		$		$
   Total cash payments		$		$		$		$
   Cash increase (decrease)		$		$		$		$
   Cash balance at end of month		$		$		$		$

   b. Are the four monthly budgets that are presented prepared as static budgets or flexible budgets?
   
   

   c. What are the budget implications for Craig Kovar?

   Craig can see that his present plan   sufficient cash. If Craig did not budget but went ahead with the original plan, he would be $   at the end of December, with no time left to adjust.

1. The Classical view, when it started and who is a good representative of this school.
2. Says Law and the assumption that Savings = Investments.
3. Explain the importance of flexible interest rates, wages and prices in this model.
4. Understand and explain the shape of the investment and savings curves. This means explain the relationship between the interest rate and savings and the interest rate and investment.

Sharpe Middle School is applying for a grant that will be used to add fitness equipment to the gym. The principal surveyed 16 anonymous students to determine how many minutes a day the students spend exercising. The results from the 16 anonymous students are shown.

0 minutes; 40 minutes; 60 minutes; 30 minutes; 60 minutes; 10 minutes; 45 minutes; 30 minutes; 300 minutes; 90 minutes; 30 minutes; 120 minutes; 60 minutes; 60 minutes; 0 minutes; 20 minutes

** Lp = (p/100) (n + 1) (the p-th percentile formula to get the location).

Determine the following five values.

Min =

Q1 =

Med =

Q3 =

Max =

If you were the principal, would you be justified in purchasing new fitness equipment?  

ANSWER:

Is/are there any potential outlier (s)?

IQR=Q3-Q1=………………………………

Lower Limit: Q1 - 1.5(IQR) =……-…………..

Upper Limit: Q3 + 1.5(IQR)=……………..

Calculating the Arithmetic Mean of Grouped Frequency Tables

When only grouped data is available, you do not know the individual data values (we only know intervals and interval frequencies); therefore, you cannot compute an exact mean for the data set. What we must do is estimate the actual mean by calculating the mean of a frequency table. A frequency table is a data representation in which grouped data is displayed along with the corresponding frequencies. To calculate the mean from a grouped frequency table we can apply the basic definition of mean: mean = data sum/number of data values.

We simply need to modify the definition to fit within the restrictions of a frequency table.

Since we do not know the individual data values we can instead find the midpoint of each interval.  

The midpoint is = (lower boundary + upper boundary)/2.

We can now modify the mean definition to be  

                   Mean of Frequency Table = Σ f m/Σ f

where f = the frequency of the interval and m = the midpoint of the interval.

Salaries for teachers in a particular elementary school district are normally distributed with a mean of $46,000 and a standard deviation of $4,900. We randomly survey ten teachers from that district. (Round your answers to the nearest dollar.)

(a) Find the 90^th percentile for an individual teacher's salary.


(b) Find the 90^th percentile for the average teacher's salary.

The mean of the population (µ) on a test that measures math skills of middle school students is 200. The variance  is 100. The test scores for the students in Mr. Petris’s class at Suburban Middle School are given below.

195        203        200               193        207               201        199               197        203               199       

195        220        200               202        200               193        205               187        218               189       

173        209        190               190        206               209        185               179        188               205

Use a rejection region with a statistical significance of 5% (p<.05) only in the upper tail.

1. What is the name of the z-test you will conduct?
2. What would be an appropriate null hypothesis that you could test using the provided information?
3. What should you conclude about the null hypothesis you developed (reject or fail to reject)? Explain.

Now use a rejection region with a total statistical significance of 5% (p<.05) incorporated in both the upper and lower tails.

4. What is the name of the z-test you will conduct?
5. What would be an appropriate null hypothesis that you could test using the provided information?
6. What should you conclude about the null hypothesis you developed (reject or fail to reject)? Explain.