1. The sample mean is an unbiased estimator for the population mean. This means:
- The sample mean always equals the population mean.
- The average sample mean, over all possible samples, equals the population mean.
- The sample mean will only vary a little from the population mean.
- The sample mean has a normal distribution.
2. Which of the following statements is CORRECT about the sampling distribution of the sample mean:
- The standard error of the sample mean will decrease as the sample size increases.
- The standard error of the sample mean is a measure of the frequency among repeated samples.
- The sampling distribution does not always follow a normal distribution even when n (the sample size) is large.
- The standard error of the sample mean will increase as the sample size increases.
3. A simple random sample (SRS) is taken from a population. Which statement is CORRECT?
- µ is an estimate of x-bar; σ is an estimate of s.
- x-bar is an estimate of µ; s is an estimate of σ.
- µ is an estimate of x-bar; s is an estimate of the standard deviation of the sample mean.
- µ is an estimate of s; σ is an estimate of x-bar.
4. Which of the following statements about confidence intervals is CORRECT? A confidence interval is:
- The estimate plus or minus the t-score.
- The parameter plus or minus the t-score times the standard error.
- The estimate plus or minus the margin of error.
- None of the above.
5. Which of the following statements about confidence intervals is WRONG?
- If we keep the sample size fixed, the confidence interval gets wider as we increase the confidence coefficient.
- A confidence interval for a mean always contains the sample mean.
- If we keep the confidence coefficient fixed, the confidence interval gets narrower as we increase the sample size.
- If the standard error increases, the confidence interval decreases in width.
6. Which of the following statements is CORRECT?
- An extremely small p-value indicates that the actual data differs markedly from that expected if the null hypothesis were true.
- The p-value measures the probability that the hypothesis is true.
- The larger the p-value, the stronger the evidence against the null hypothesis
- The p-value measures the probability that the sample mean is more than the population mean.
7. The average time it takes for a person to experience pain relief from aspirin is 25 minutes. A new ingredient is added to help speed up relief. Let µ denote the average time to obtain pain relief with the new product. An experiment is conducted to verify if the new product is better. What are the null and alternative hypotheses?
- H0: µ = 25
- HA: µ < 25
- H0: µ < 25
- HA: µ = 25
- All of the above is correct since both the null and alternative hypotheses can be set up arbitrarily.
8. Suppose you are conducting a two sample significance testing. The null hypothesis states that
- The samples come from populations with different means
- The samples have the same sample mean
- The samples have very different sample means
- The samples come from populations with the same mean
9. In a random sample of 100 individuals, 12 are left-handed. Which of the following is a plausible 95% confidence interval for the proportion of left-handed people in the population?
- 0.056 to 0.184
- 0.037 to 0.103
- 0.056 to 0.084
- 0.120 to 0.240
DEFINITION:
- Margin of Error:
- Error:
- Alternative Hypothesis:
- Significance:
SHORT ANSWER:
- To test the effect of the policy, you would compare the test scores before and after the implementation using simple regression analysis. The dependent variable would be the test scores and the independent variable would be the implementation of the policy. The null hypothesis would be that there is no effect of the policy (β = 0) and the alternative hypothesis would be that there is a significant effect of the policy (β ≠ 0).
- The mean income of $44,776 and the median income of $35,680 are statistics because they are calculated from a sample.
- To say that we have "95% confidence" in this interval means that if we were to repeat the sampling process and construct a confidence interval in the same way, 95% of the intervals would contain the true population parameter.
- The 95% confidence interval for the percent of all adults who want to lose weight would be calculated using the sample proportion and the margin of error.
- The statement that results are significant because they cannot easily be explained by chance variation alone is essentially correct. Statistical significance indicates that the observed results are unlikely to have occurred by chance alone.
- The percentage of the time that the trip will take less than 60 minutes can be calculated by finding the z-score for 60 minutes and using the standard normal distribution table.
- To determine if 100 minutes is an unusually long commuting trip, you would calculate the z-score for 100 minutes and compare it to the standard normal distribution table to find the corresponding percentage.
- The regression equation for the above output would be: TRAVELTIME = 21.754 + 1.595(Work Disability)
- The constant in the regression output gives the average travel time to work for a person without a disability.
- The slope in the regression output gives the difference in travel time to work between disabled persons and those who are not disabled.
- The null hypothesis would be that disabled people earn the same as non-disabled people (β = 0) and the alternative hypothesis would be that disabled people earn less than non-disabled people (β < 0).
- To determine if disabled people earn less than non-disabled people at the 5% significance level, you would compare the p-value to the significance level (0.05).
- To determine if disabled people earn less than non-disabled people at the 1% significance level, you would compare the p-value to the significance level (0.01).