Math Test 4 (Ch. 19-23)

Sampling methods and confidence intervals are routinely used for financial audits of large companies. Which of the following is an advantage of doing it this way versus having a complete audit of all records?

- A sample can be done more carefully than a complete audit. - A well-designed sampling audit may yield a more accurate estimate than a less carefully carried out complete audit or census. - It is much cheaper.

Suppose you computed a 95% confidence interval for the difference in mean weight between two species of snakes in a large nature reserve (species #1 − species #2), and your interval is −3.6 to 61.6 ounces. What can you conclude?

- If we were willing to use 90% confidence, we could say that the observed difference in the sample means represents a real difference in the population means. - Because the interval extends so much further in the positive direction than the negative, the evidence suggests that species #1 weighs more than species #2 on average, but we can't say for sure. - You cannot say, even with 95% confidence, that the observed difference in sample means represents a real difference in the population means.

Which of the following statements is true regarding a 95% confidence interval? Assume numerous large samples are taken from the population.

- In 95% of all samples, the sample proportion will fall within 2 standard deviations of the mean, which is the true proportion for the population. - If we add and subtract 2 standard deviations to/from the sample proportion, in 95% of all cases we will have captured the true population proportion. - In 95% of all samples, the true proportion will fall within 2 standard deviations of the sample proportion.

Which of the following describes the power of a test?

- It is the probability of making the correct decision when the alternative hypothesis is true. - It is higher when the population value is farther from the value in the null hypothesis. - Bigger samples result in more power for the test, and smaller samples result in less power for the test.

No matter what type of population value (or combination of population values) is being estimated using a confidence interval, what items should you be watching for in order to best assess the results?

- That any real differences for which the researchers imply a causal relationship came from a randomized experiment. - That the sample(s) selected represent the population(s). - That the confidence level is clearly stated.

Which of the following is true when a Type I error has been committed?

- The data must have convinced us that the alternative hypothesis was true. - The null hypothesis has to have been true. - The probability of making a Type I error is equal to the stated level of significance, usually 0.05.

When a relationship or value from a sample is so strong that we decide to rule out chance as an explanation for its magnitude, what does this mean?

- We conclude that the observed result carries over to the population and cannot be explained away by chance. - We could have been unlucky with our sample, and come to the wrong conclusion, but that chance is small. - The observed result is statistically significant.

Suppose a 95% confidence interval for the difference in test scores between Class 1 and Class 2 (in that order) is the following: 9 +/− 2. These results were based on independent samples of size 100 from each class. What can you conclude?

- You are confident that the average for Class 1 was 7 to 11 points higher than for Class 2. - You are confident that the observed difference found in the two samples (plus or minus the margin of error) will carry over to their respective populations. -You are confident that the averages for Class 1 and Class 2 are significantly different.

Suppose that test scores on a particular exam have a mean of 77 and standard deviation of 5, and that they have a bell-shaped curve. Suppose you take numerous random samples of size 100 from this population. Describe the shape and give the mean and standard deviation of the resulting frequency curve. The resulting frequency curve would have a (BLANK) graph with a mean of (BLANK) and a standard deviation of (BLANK).

1. Bell-Shaped Graph 2. 77 3. 0.5

Suppose a survey was conducted to find out what proportion of Americans intend to vote in the next Presidential election. For which of the following confidence intervals would it be fair to conclude, with high confidence, that a majority of Americans will vote in the next Presidential election?

52% plus or minus 1%

What is the most common level of confidence used to construct confidence intervals?

95%

Which of the following are examples where you would be interested in estimating the population mean?

About how long do left-handed people live?

Suppose instead of comparing independent measurements taken from two groups, you used a matched-pairs experiment and one treatment is randomly assigned to each half of the pair. In this case, how should you compute the confidence interval for the difference?

Compute the differences for each pair, treat them as a single data set, and use the formula for a confidence interval for one mean (the mean difference).

Which of the following statements is false?

Confidence intervals are always close to their true population values.

Suppose a confidence interval for the difference in mean weight loss for two different weight loss programs (Program 1 − Program 2) is entirely above zero. What does this mean?

We can say with confidence that there is a difference in mean weight loss for the populations of people on these two programs; further, we can say that the average weight loss on Program 1 is higher.

Suppose that test scores on a particular exam have a mean of 77 and standard deviation of 5, and that they had a bell-shaped curve. Suppose that the test scores are no longer bell-shaped, but are skewed to the right. You want to take a random sample and estimate the average test scores for this population. You want to be able to use the rule of sample means to interpret your results in this case. Under what (if any) conditions is this possible?

You can use it only if the sample is large enough (at least 30)

Suppose a 95% confidence interval for the difference in test scores between Class 1 and Class 2 (in that order) is the following: 9 +/− 2. These results were based on independent samples of size 100 from each class. Now suppose you switch the order of Class 1 and Class 2 in your analysis but keep the data labeled correctly in terms of which class they came from. Which of the following statements is false?

You can't do it this way. You'll get negative numbers for the difference in the means and/or negative numbers for the standard error

If numerous large random samples or repetitions of the same size are taken from a population, the frequency curve made from proportions from the various samples will have what approximate shape?

a bell shape

When someone reports that their results are found to be 'statistically significant', which type of statistical technique was most likely used?

a hypothesis test

What numerical value do you calculate that gives you the answer to the question of how unlikely the test statistic would be if the null hypothesis were true?

p-value

If numerous large random samples or repetitions of the same size are taken from a population, the proportions from the various samples will have what approximate mean?

the true population proportion