A school principal is interested in assessing the performance of her students on the Totally Oppressive Standardized test (TOST). She selects a simple random sample of 16 of her students and finds the following set of test scores:

Assume that the sample is drawn from a population with a standard deviation σ = 7.20.

a. (1 point) What is the mean test score for the sample of students?

13

b. (4 points) Calculate and write a sentence to interpret the 95% confidence interval for the mean test score.

c. (3 points) Calculate and write a sentence to interpret the 99% confidence interval for the mean test score.

13 - 2.58 * (1.8) 13 + 2.58 * (1.8)= 8.3,17.6????

d. (4 points) Explain why the margin of error for the 95% confidence interval in question (b) is smaller than the margin of error for the 99% confidence interval in question (c).

Suppose that the daily consumption of Pepsi in ounces by a high school student is normally distributed with mean = 13.0 ounces and variance = 2.0 ounces. The daily amount consumed is independent of other days except adjacent days where the covariance is -1.0. If the student has two six-packs of 16 ounce Pepsi bottles, what is the probability that some Pepsi remains at the end of two-weeks ?

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 $   at the end of December, with no time left to adjust.

The weight (in pounds) for a population of school-aged children is normally distributed with a mean equal to 138 ± 23 pounds (μ ± σ).Suppose we select a sample of 100 children (n = 100) to test whether children in this population are gaining weight at a 0.05 level of significance.

• Part (a)

  What are the null and alternative hypotheses?

  H₀: μ = 138
  H₁: μ < 138

• H₀: μ = 138

• H₁: μ ≠ 138    

• H₀: μ ≤ 138

• H₁: μ > 138

• H₀: μ ≤ 138
  H₁: μ = 138

• Part (b)

  What is the critical value for this test?

• Part (c)

  What is the mean of the sampling distribution?
  lb

• Part (d)

  What is the standard error of the mean for the sampling distribution?
  lb

A random selection of students at a school were chosen at random and how long they spent eating compared to how many calories they consumed was recorded as the following:

1. Make a scatterplot for the data

2. Find the LSRL

3. Describe the slope and the y-intercept, do they make sense?

4. Create a Residual Plot for the data

5. Create a 95% confidence interval for the slope of the line

A random selection of students at a school were chosen at random and how long they spent eating compared to how many calories they consumed was recorded as the following:

1. Make a scatterplot for the data

2. Find the LSRL

3. Describe the slope and the y-intercept, do they make sense?

4. Create a Residual Plot for the data

5. Create a 95% confidence interval for the slope of the line

A school is conducting optimization studies of the resources it has. One of the principal concerns of the Director is that of the staff. The problem he is currently facing is with the number of guards in the "Emergencies" section. To this end, he ordered a study to be carried out that yielded the following results:

Time Minimum number of guards required
O to 4 40
4 to 8 80
8 to 12 100
12 to 16 70
16 to 20 120
20 to 24 50

Each guard, according to Federal labor law, must work eight consecutive hours per day. Formulate the problem of hiring the minimum number of guards that meet the above requirements, as a Linear programing model. 

At the local high school, there are 297 students. 71 students are seniors, and out of the 71 students, 53 participate in a sport (while 18 do not participate in a sport). Among those who are not seniors, 69 students participate in a sport and 157 do not. Suppose we choose one student at random from the entire class.

A. Are events "drawing someone who is a senior" and "drawing someone who does not play a sport" mutually exclusive? Why/why not?

B. Are events "drawing someone who is a senior" and "drawing someone who does not play a sport" independent? Why/why not?

(C-E) Suppose you draw five students at random without replacement.

C. What is the conditional probability that the second student drawn is a senior, if the first student drawn is a senior?

D. What is the probability that the second student drawn is a senior, without knowing anything about the first student?

E. What is the probability that among the five students, one of them is a senior?