# Statistics

1. An appropriate 95% confidence interval for mu has been calculated as (- 0.73, 1.92) based on n = 15 observations from a population with a normal distribution. The hypotheses of interest are H0 : mu = 0 versus Ha: mu <> 0. Based on this confidence interval ...

3. An analyst, using a random sample of n = 500 families, obtained a 90 percent confidence interval for mean monthly family income for a large population: ($600, $800). If the analyst had used a 99 percent confidence coefficient instead, the confidence interval would be ...

4. A Gallup poll of a sample of 1089 Canadians (total population of 26,000,000) found that about 80% favored capital punishment. A Gallup poll of a sample of 1089 Americans (total population of 260,000,000) also found that 80% favored capital punishment. Which if the following statements is TRUE?

5. A 95% confidence interval for mu is calculated to be (1.7, 3.5). It is now decided to test the hypothesis H0 : mu = 0 vs HA:mu <> 0 at the alpha = 0.05 level, using the same data as was used to construct the c.i ...

6. In a statistical test for the equality of a mean, such as H0 : mu = 10, if alpha = 0.05, then ...

7. In hypothesis testing, beta is the probability of committing an error of Type II. The power of the test, 1 − beta is then ...

8. Resting pulse rate is an important measure of the fitness of a person's cardiovascular system with a lower rate indicative of greater fitness. The mean pulse rate for all adult males is approximately 72 beats per minute. A random sample of 25 male students currently enrolled was selected and the mean pulse resting pulse rate was found to be 80 beats per minute with a standard deviation of 20 beats per minute. The experimenter wishes to test if the students are less fit, on average, than the general population. A possible Type II error would be to:

9. During the pre-flight check, Pilot Jones discovers a minor problem - a warning light indicates that the fuel gauge may be broken. If Jones decides to check the fuel level by hand, it will delay the flight by 45 minutes. If Jones decides to ignore the warning, the aircraft may run out of fuel before it gets to Gimli. In this situation, what would be the appropriate null hypothesis? The type I error?

10. 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 mu 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?

11. The sample mean is an unbiased estimator for the population mean. This means:

12. What is a statistical inference?

13. Does playing music to dairy cattle increase their milk production? An experiment was conducted where a group of dairy cattle was divided into two groups. Music was played to one group; the control group did not have music played. The average increase in production was 2.5 l/cow over the time period in question. A 95% confidence interval for the difference (treatment-control) in the mean production was computed to be (1.5,3.5) l/cow. This means:

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#### Solution Preview

Research and Evaluation Class

1. An appropriate 95% confidence interval for mu has been calculated as (- 0.73, 1.92) based on n = 15 observations from a population with a normal distribution. The hypotheses of interest are H0 : mu = 0 versus Ha: mu <> 0. Based on this confidence interval,

Does this mean that the null hypothesis is mu = 0 and the alternative hypothesis is mu ≠ 0? If so ...

The confidence interval is (-0.73, 1.92). It contains 0. Because the CI contains 0, you cannot reject the null hypothesis that mu = 0. Therefore, there is no evidence to suggest that mu is different than 0.

2. Recall in one assignment you surveyed cars in a parking lot to estimate the proportion that were red or the proportion that were from a Japanese manufacturer. Which of the following is NOT CORRECT?

a. A sample of 100 cars in a convenience sample is always better than a sample of 20 cars from a proper random sample.

This is not correct -- the 100 cars in a convenience sample might not be better. The sample might be biased (see question 11) and not be a good estimate of the population mean.

b. A convenience sample of the cars closest to the Applied Science building may give a biased estimate of the proportion of cars which are from a Japanese manufacturer.

Correct -- the people who park near the Applied Science building might not be representative of the population as a whole.

c. A sample of 100 cars from a proper random sample will give more precise estimates of the proportion of cars that are red than a sample of 20 cars from a proper random sample.

Correct -- larger samples are better (if everything else is the same, i.e. both are random samples).

d. The sample proportion of cars that are red is an unbiased estimate of the population proportion if the sampling is a simple random sample.

Correct.

e. Different students may get different answers for the proportion of cars that are red.

Correct -- they might get very different proportions just based on chance.

3. An analyst, using a random sample of n = 500 families, obtained a 90 percent confidence interval for mean monthly family income for a large population: ($600, $800). If the analyst had used a 99 percent confidence coefficient instead, the confidence interval would be:

a. wider but it cannot be ...