Question

4.A claim is made that 25% of American college students leave the United States during spring break. You believe this claim is incorrect. You would like to test the null hypothesis that ? = 0.25 versus the alternative hypothesis that ? ≠ 0.25. You gather data from a random sample of 100 college students and obtain a test statistic of 1.8. If we assume the significance (or alpha) level is α = 0.05, what should your decision be? A. Reject the null hypothesis B. Fail to reject the null hypothesis C. Reject the alternative hypothesis D. Fail to reject the alternative hypothesis E. We cannot reach a conclusion without knowing the sample proportion.

5. An engineer designs an improved light bulb. The previous standard light bulb design had an average lifetime of 1200 hours. When a random sample of n = 40,000 new light bulbs was tested, it was found that the new light bulbs had an average lifetime of 1201 hours. Although the difference between 1200 and 1201 is quite small, it is a statistically significant difference. The most likely explanation for this statistically significant difference is that A. the average of 1201 is large. B. the sample size of 40,000 is large. C. the new light bulb designs typically have more variability than the standard light bulb designs. D. all of the above are likely explanations.

6. Perchlorate is a chemical used in rocket fuel. People who live near a former rocket-testing site are concerned that this chemical is present in unsafe amounts in drinking water. To be considered safe, driving water should have an average perchlorate level of 24.5 parts per billion (ppb) or less. A random sample of 75 water sources in this area shows a mean perchlorate level of 25.3 ppb. If we use this information to conduct a hypothesis test, what should the alternative hypothesis be? A. µ < 25.3 B. µ > 25.3 C. µ < 24.5 D. µ > 24.5 E. µ ≠ 24.5

Answer 1

4. Here test statistics is 1.8

As it is two tailed test we get P value as

As P value is greater than alpha=0.05

Hence we fail to reject the null hypothesis

So answer is B. Fail to reject the null hypothesis

5. As the same size is too large, data is statistically significant

So answer here is B. the sample size of 40,000 is large.

6. Here claim is that driving water should have an average perchlorate level of 24.5 parts per billion (ppb) or less.

So alternative hypothesis is

Hence alternative hypothesis is D. µ > 24.5