In: Statistics and Probability
1. The length of human pregnancies from conception to birth varies according to a distribution that is approximately Normal with mean 266 days and standard deviation 16 days. About 68% of all pregnancies last between
a. 250 and 282 days b. 234 and 298 days c. 218 and 314 days d. 250 and 266 days
2. The distribution of actual weights of chocolate bars produced by a certain machine is approximately Normal with mean 8.2 ounces and standard deviation of 0.1 ounces. What proportion of chocolate bars weigh under 8 ounces?
a. 13.5% b. 34% c. 16% d. 2.5%
3. Sixteen weighings of a small object on a sensitive scale result in 5.15 grams 4 times, 5.35 grams 4 times, 5.20 grams, 4 times and 5.30 grams 4 times, 16 total. If the standard deviation σ of weighings on this scale is .8 grams, what is an approximate 95% confidence interval for the true weight of the object?
4. A survey of 900 gun-owners who frequent a popular shooting range in Texas had a nearly 100% response rate. If only 18% of the respondents thought more laws on gun control should be enacted, the conclusion that less than 20% of people in the region support more gun laws would certainly be dubious due to which of the following?
a. large standard deviation of samples of size 900 b. nonresponse from the sample
c. sampling bias of respondents d. small sample size
5. Scores on a test for 8th graders range from 0 to 500. In a SRS of 400 students, the mean score is 335 and the standard deviation is 70. The standard deviation of the sampling distribution of x̅400 is what?
6.The weights of a sample of 400 2-year-olds in Kentucky yields
x̅400 is 21.2 pounds with a standard deviation of σ = 3
pounds. What is a 95% confidence interval for the weight of all
two-year-olds in Kentucky?
a. 18.2-21.5 pounds b. 15.2-27.2
pounds c. 21.185-22.015
pounds d. 20.9-21.5 pounds
7.When finding confidence intervals, the interval is smaller if
a.sample size and standard deviation are bigger b.sample size and standard deviation are smaller
c.sample size is bigger, but the standard deviation is smaller d.sample size is smaller, but standard deviation is bigger.
8. If the birth weights of the babies born annually in a hospital is Normal with a mean of 5 pounds 10 ounces and a standard deviation of 5 ounces, what percentage of babies are born weighing less than 5 pounds? (No table needed.)
a. 13.5% b. 2.5% c. 16% d. .3%
9. What percent of the babies born weigh between 5 pounds and 5 pound 5 ounces? (Again no table.)
a. 13.5% b. 47.5% c. 16% d. 34%
10. Of the 40 babies born during the first weeks of next month, how many are likely to be under five pounds?
a. 4 b. 2 c. 6 d. 1
11.) A random sample of 1,600 adults in a certain country shows that 72% have smart phones. What is a 80% confidence interval for the percentage of adults having smart phones in this country?
12.If 48% of the 400 voters sampled voted for candidate A over candidate B, what is a 95% confidence for p hat, the estimate for the percentage candidate p that A would receive?
13.Twenty-five randomly selected students are asked how many times a month they eat pizza. The average for this sample is x̅25= 11.75 times,but the population mean of all college students is claimed to be μ = 10.60 times. If the null hypothesis is H0 is μ = 10.60 times and the standard deviation σ = 5 times, should the null hypothesis be rejected at the 5% level of significance? (No table needed)
14. Is the distribution of incomes in the US described by a normal distribution with μ equal to the mean income?
15. The weights of baby orangutans has standard deviation 4 pounds. How large a sample of baby orangutans is necessary for the 95% margin of error to be .5 pounds?
a. 144 b. 324 c. 256 d. 900
16. A car manufacturer says their cars average 26 miles per gallon of gas at 65 miles per hour a standard deviation of σ = 2 miles per gallon.. A Consumer group tested 100 such cars and found the average x̅100 to be 25.4 miles per gallon. Is this sufficiently small to reject the null hypothesis H0: μ = 26 miles per gallon? (No table needed.)
a. Yes b. No c. Not enough information.
17. What is the probability that z, the standard normal distribution, is less than 1.75 standard deviations below the mean of zero?
a. 5% b. 4% c. 6% d. 7.4%
18. If two random samples of the heights of adult males in New York are taken, one of 400, the other of 900 people, which one would likely have the larger range from shortest to tallest?
a. the 400 person sample b. the 900 person sample c. they’d be equal
19. The p-value of a test of the null hypothesis is 3.5%. This means
a. the hypothesis is true with probability 3.5% or possibly less than 3.5% b. the alternative hypothesis is true with probability 3.5% or possibly less c. 3.5% is the probability of finding the observed or more extreme results when the null hypothesis (H 0) is true d. None of the above
20. One of the main reasons to be interested in the regression line of y on x is that
a. one can use it to predict y-values from different x-values b. one can determine the standard deviation of y
c. one can determine from it the values of the quartiles of x and y.