STATISTICAL SOLUTION

Note: in deciding between doing a z-test or a t-test consider the main criteria the size of the sample. If the sample size is small (<30) perform a t-test, if the sample size is larger (>= 30) perform a z-test.
Similar conditions for two sets tests.

Q1. (10 POINTS)
For each of the following claims mention what type of test should be used (one-tail, two-tail) and set up the null and alternate hypothesis.
Consider that the critical value is = CV. For each H0, mentioned the acceptance range.

a) The 87Cents Store claims that their daily profit is more than $5000.

b) The Pastry shop claims that its chocolate cookies at least 50% chocolate per cookie.
c) PS193 claims that its students scored in the 96thile.

Q2. (22 POINTS)
A researcher wishes to test the claim that the average cost of tuition and fees at a 4-year college less than $7000. She selects a random sample of 81 colleges and finds the mean to be $6950. The standard deviation is $500.
a. Is there evidence to support the claim at α = .04?

b. Suppose no claim was made but the researcher is thinking of making a claim using a 95% two-sided confidence interval. Using the same data, construct the CIE interval.

Q3. (13 POINTS) An educator claims that the average salary of substitute teachers in New York Isa most $100 per day. A random sample of ten school districts is selected, and the daily salaries are shown. Is there evidence to support the claim at α = .01?

85
70
110
95
90
102
87
78
69
100

Q4.(15 POINTS) A professor claims that the average of scores obtained by Mathematics majors is close to the average of scores obtained by the Computer Science majors. At α = .05 is there enough evidence to support the claim?

Mathematics majors: Average score = 83 standard deviation = 5 n1 = 10
Computer Science majors: Average score = 79 standard deviation = 4 n2 = 15

Q5. (10 POINTS) Consider the following excel regression analysis output.
Explain the significance of the r, p, F value; Give the regression equation.

Q6. (30 POINTS) One of the stores is a proud sponsor of the college soccer team. They constantly try to raise money for the team and they want to determine if there is any type of relationship between the amount of contribution and the years that the alumnus has been out of school.
Note: the scatter plot might give you all the necessary information.

Years (X)
1
5
3
10
6
6
2

Contribution (Y)
250
100
110
0
70
80
175

a. Using Excel construct a scatter plot. Discuss the output of the scatter plot.
The scatter plot indicates a negative relationship between the variables. As years increase, the contribution decreases and vice versa. The points appear to form a linear line.
b. Give (or calculate) the correlation coefficient.
c. Give (or calculate) the coefficient of determination.
d. Give (or calculate) the regression equation coefficients; Give the equation of regression.
e. (very important)
Based on the above values, in detail draw the conclusion:
• Discuss the correlation coefficient r
• Discuss the coefficient of determination r2
• Discuss in detail the meaning of the regression equation
e. How much would be the contribution of a student who graduated 8 years ago?
f. After how many years after graduations the alumni will stop contributing.