Question 1

A random sample of 20 SAT scores is listed below. Calculate the sample mean and standard deviation

1005, 1032, 940, 994, 967, 980, 1017, 1020, 1000, 1040, 1038, 1035, 925, 984, 999, 1001, 1002, 1027, 986, 996

(a) 995, 29.90

(b) 996, 31.31

(c) 999.4, 30.74

(d) 1001, 30.26

Question 2

Given SAT scores are approximately normally distributed with a mean of 1000 and standard deviation of 25, the proportion of people with SAT scores above 1049 is:

(a) 95%

(b) 5%

(c) 68%

(d) 2.5%

Question 3

Failing to reject the null hypothesis when it is false is called:

(a) Beta

(b) Alpha

(c) Type I Error

(d) Type II Error

Question 4

The probability of Messi scoring a goal in a match at La Liga is 65%. Assuming a Binomial model, what is the probability that Messi scores in 3 of the next 5 matches?

(a) 60%

(b) 18.11%

(c) 30%

(d) 33.6%

Question 5

The P-value for a right-tailed test is p=0.034. Which of the following is correct?

(a) The p-value for a left-tailed test based on the same sample would be p=-0.034

(b) We would reject the null hypothesis at the significance level at 5% but not at 1%

(c) The p-value for a two-tailed test based on the same sample would be p=0.060

(d) We would reject the null hypothesis at the significance level at 1% but not at 5%

Question 6

At a college, the probability that a student studies statistics and business in the same semester is 0.05. The probability that a student takes statistics is 0.25. The probability that a student is studying business, given that she is studying statistics is:

(a) 20%

(b) 25%

(c) 5

(d) 40%

Question 7

For any data set, we can ascertain that half of the observations are less than the

(a) Mode

(b) Standard Deviation

(c) Median

(d) Mean

Question 8

A sample of 200 light bulbs manufactured by Phelps Ltd found that 24 had a defect. A 95% confidence interval for the proportion of all Phelps light bulbs with a defect is 0.032 to 0.091. Which of the statements below best describe the correct interpretation of the confidence interval.

(a) If a large number of samples are drawn for the proportion of light bulbs with defect and a confidence interval is constructed, 95% of these intervals would contain the proportion of light bulbs with defect.

(b) Any random sample of size 200 will have a proportion of 0.091 of defect bulbs.

(c) None of the above

(d) The probability that the proportion of light bulbs with defect is between 0.032 and 0.091 is 95%.

Question 9

A coffee machine can be adjusted to deliver any xed number of millilitres of coffee. If the machine is operating with a standard deviation in delivery equal to 1.3 millilitres, what should be the mean setting so that a 12-millilitre cup will overow less than 5% of the time? Assume a normal distribution for millilitres delivered.

(a) 10.70 millilitres

(b) 13.30 millilitres

(c) 14.05 millilitres

(d) 9.95 millilitres

Question 10

For the standard normal probability distribution, the area to the left of the mean is

(a) None of the above

(b) 0.5

(c) Greater than 0.5

(d) Less than 0.5

Question 11

The travel time for a tourist traveling between Johannesburg and Cape Town is uniformly distributed between 720 and 840 minutes. The probability that he will finish his trip in 800 minutes or less is approximately:

(a) 50%

(b) 80%

(c) 67%

(d) 33%

Question 12

A standard normal distribution is a normal distribution with the following parameters:

(a) Mean of 0 and standard deviation of 1

(b) Any mean and any standard deviation

(c) Mean of 0 and standard deviation of 0

(d) Mean of 1 and standard deviation of 0