Question

1. Private colleges and universities rely on money contributed by individuals and corporations for their operating expenses. Much of this money is invested in a fund called an endowment, and the college spends only the interest earned by the fund. A recent survey of eight private colleges in the United States revealed the following endowments (in millions of dollars): 60.2, 47.0, 235.1, 490.0,

22.6, 177.5, 95.4, and 220.0. Summary statistics yield x = 180.975 and s = 143.042. Calculate a 99%

confidence interval for the mean endowment of all private colleges in the United States. Note that s is sample standard deviation.

A) 180.975 ± 181.387                                                             B) 180.975 ± 169.672

C) 180.975 ± 176.955                                                             D) 180.975 ± 189.173

2) An educator wanted to look at the study habits of university students. As part of the research, data was collected for three variables - the amount of time (in hours per week) spent studying, the amount of time (in hours per week) spent playing video games and the GPA - for a sample of 20 male university students. As part of the research, a 95% confidence interval for the average GPA of all male university students was calculated to be: (2.95, 3.10). The researcher claimed that the average GPA of all male students exceeded 2.94. Using the confidence interval supplied above, how do you respond to this claim?

A) We are 95% confident that the researcher is correct.

B) We are 95% confident that the researcher is incorrect.

C) We are 100% confident that the researcher is incorrect.

D) We cannot make any statement regarding the average GPA of male university students at the 95% confidence level.

3) A retired statistician was interested in determining the average cost of a $200,000.00 term life insurance policy for a 60-year-old male non-smoker. He randomly sampled 65 subjects

(60-year-old male non-smokers) and constructed the following 95 percent confidence interval for the mean cost of the term life insurance: ($850.00, $1050.00). State the appropriate interpretation for this confidence interval. Note that all answers begin with "We are 95 percent confidence that…"

A) The term life insurance cost of the retired statistician's insurance policy falls between $850.00 and $1050.00

B) The average term life insurance cost for sampled 65 subjects falls between $850.00 and

$1050.00

C) The term life insurance cost for all 60-year-old male non-smokers' insurance policies falls

between $850.00 and $1050.00

D) The average term life insurance costs for all 60 -year-old male non-smokers falls between

$850.00 and $1050.00

4) How many tissues should a package of tissues contain? Researchers have determined that a person uses an average of 41 tissues during a cold. Suppose a random sample of 10,000 people yielded the following data on the number of tissues used during a cold: x = 35, s = 18. Identify the null and

alternative hypothesis for a test to determine if the mean number of tissues used during a cold is

as claimed.

A) H0: μ > 41 vs. Ha: μ ≤ 41                                                B) H0: μ = 41 vs. Ha: μ ≠ 41

C) H0: μ = 41 vs. Ha: μ < 41                                               D) H0: μ = 41 vs. Ha: μ > 41

5) A local eat-in pizza restaurant wants to investigate the possibility of starting to deliver pizzas. The owner of the store has determined that home delivery will be successful only if the average time spent on a delivery does not exceed 37 minutes (no morwe). The owner has randomly selected 15 customers

and delivered pizzas to their homes. What hypotheses should the owner test to demonstrate that the pizza delivery will not be successful?

A) H0: μ = 37 vs. Ha: μ < 37                                                B) H0: μ < 37 vs. Ha: μ = 37

C) H0: μ ≤ 37 vs. Ha: μ > 37                                                D) H0: μ = 37 vs. Ha: μ ≠ 37

6) Researchers have claimed that the average number of headaches per student during a semester of Statistics is 11. In a sample of n = 16 students the mean is 12 headaches with a deviation of 2.4. Which of the following represent the null and alternative hypotheses necessary to test the students' belief?

A) H0: μ = 11 vs. Ha: μ > 11                                                B) H0: μ = 11 vs. Ha: μ < 11

C) H0: μ < 11 vs. Ha: μ = 11                                               D) H0: μ = 11 vs. Ha: μ ≠ 11

Answer 1

1)

A survey of eight private college has taken

Thus n = 8

. Summary statistics yield = 180.975 and s = 143.042.

Calculate a 99% confidence interval for the mean endowment of all private colleges in the United States.

Now 99% confidence interval is given by

CI = { * SE }

Now is t-distributed with n-1 = 8-1 = 7 degree of freedom and =0.01,

It can be computed from statistical book or more accurately from any software like R,Excel

From R

> qt(1-0.01/2,df=7)
[1] 3.499483

Thus = 3.499483

SE = =    = 50.57298

Thus 99% confidence interval is

CI = { * SE } = { 180.975 3.499483 *50.57298 } = { 180.975 176.9793 }

Thus correctect option is

Option C) 180.975 ± 176.955

2)

data was collected for three variables - the amount of time (in hours per week) spent studying , the amount of time (in hours per week) spent playing video games and the GPA - for a sample of 20 male university students.

A 95% confidence interval for the average GPA of all male university students was calculated to

be: (2.95, 3.10).

The researcher claimed that the average GPA of all male students exceeded 2.94.

Which means that average GPA of all male students are greater than 2.94 and also our confidence interval (2.95, 3.10) is greater than 2.94. So our claim is true.

Correct option is

A) We are 95% confident that the researcher is correct.

3)

95 percent confidence interval for the mean cost of the term life insurance: ($850.00, $1050.00).

Hence correct option is

D) The average term life insurance costs for all 60 -year-old male non-smokers falls between

$850.00 and $1050.00

"We are 95 percent confidence that the average term life insurance costs for all 60 -year-old male non-smokers falls between $850.00 and $1050.00 "

4)

Researchers have determined that a person uses an average of 41 tissues during a cold.

Since here we are not testing the cliam that weather mean number of tissues used during a cold is less than 41 or greater than 41 , so this is two tail test ( i.e we need to test weather person uses an average of 41 tissues during a cold or not )

Correct option is ,

B) H0: μ = 41 vs. Ha: μ ≠ 41

5)

The owner of the store has determined that home delivery will be successful only if the average time spent on a delivery does not exceed 37 minutes (no morwe).

So here if time spent on a delivery is greater than 37 , then it will not be succesful.

So hypotheses should the owner test to demonstrate that the pizza delivery will not be successful is

C) H0: μ ≤ 37 vs. Ha: μ > 37 .

If we fail to reject null hypothesis then it implies than home delivery is successful , otherwise if we reject null hypothesis H0 , then we can conclude than home delivery may not be successful

6)

Researchers have claimed that the average number of headaches per student during a semester of Statistics is 11.

Since here we are not testing weather number of headaches per student is more or less than 11 , so these is two tail test . The claim is that the average number of headaches per student is 11 , so we wish to check weather it is 11 or not .

Correct option is

D) H0: μ = 11 vs. Ha: μ ≠ 11