Question

i. A researcher estimated the proportion of voters who favor the Democratic candidate in an election. Based on 500 people she calculates the 95% confidence interval for the population proportion p:   0.123 <p<0.181.

Which of the following is a valid interpretation of this confidence interval ?______

a. There is a 95% chance that the true value of p lies between 0.123 and 0.181

b.   If many different samples of 500 were selected and a confidence interval was constructed based on that sample, in the long run 95% of the confidence intervals would contain the true value of p.

c.   If 100 different samples of 500 were selected and a confidence interval was constructed based each sample, exactly 95 of these confidence intervals would contain the true value of p.

ii. Given a p-value of 0.083, Do you reject or fail to reject the null hypothesis at   ______

     the .05 significance level?

a. reject the null hypothesis

b. fail to reject the null hypothesis

c. not enough information to decide

iii. A significance test will be performed to determine whether the mean daily ______ temperature is less this summer than last summer.

a. A lower-tail test should be used

b. A upper-tail test should be used.

c. A two-sided test should be used.

d. The type of test cannot be determined because the sample mean is unknown.

iv. Suppose that all the values in a data set are converted to z-scores. Which of the following statements is true?

a. The mean and the standard deviations of the z-scores will be the same as the original data.

b. The mean of the z-scores will be zero and the standard deviation will be one.

c. Both the mean and standard deviation of the z-scores will be zero.

v. Find the margin of error given the following: 99% confidence interval;

n = 68, x bar = 4156 and Std dev. = 839. ________

a. 1298    b.   237    c. 262    d. 8

vi. When do Type II errors occur?________

a. We decide to reject the null hypothesis when the null hypothesis was actually true.

b.   We fail to reject the null hypothesis when the null hypothesis is actually false.

c.   They occur in both cases.

vii. A standard score of z = 1.00 for an observation means: _________

a. The mean of the distribution lies 1 standard deviations below the observation.

b. The observation lies 1 standard deviations below the mean.

c. The observation lies 1 standard deviations above the mean.

d. The observation lies 1 means below the standard deviation.

viii. Given a 90% and a 95% confidence interval, which of the following is true?

1.   The 90% confidence interval is wider than the 95% confidence interval.
2. There is a better chance that the true mean will be found in the 95% confidence interval.

3. None of the above.

ix. The number of hours per week that high school juniors watch TV is normally distributed with a mean of 8 hours and a standard deviation of 2 hours. If 100 students are chosen at random, find the probability that the mean for that sample is between 8.2 and 8.8

1. 0.1598     b. 0.1586     c. 0.1156    d. 0.1152

Note: standard deviation/ the square root of n.

Check out the Central Limit Theorem

Answer 1

Basic concept of statistical inference