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# Math Week 8 Assignment Elementary Statistics

• From Mathematics, Statistics
• Due on 02 May, 2019 05:59:00
• Asked On 27 Apr, 2019 02:40:08
• Due date has already passed, but you can still post solutions.
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For the test of significance questions, clearly indicate each of the formal steps in the test of significance.
Step 1: State the null and alternative hypothesis.
Step 2: Calculate the test statistic.
Step 3: Find the p-value.
Step 4: State your conclusion. (Do not just say “Reject H0” or “Do not reject H0”, state the conclusion
in the context of the problem.)

1. A market research group is interested in comparing the mean weight loss for two different popular diets.
The researcher chooses two random samples of participants for the two diet programs. For Diet A, the
mean weekly weight loss for 10 participants was 1.5 pounds with standard deviation 0.4 pounds. For Diet
B, the mean weekly weight loss for 12 participants was 1.2 pounds with standard deviation 0.6 pounds. At
a 5% significance level, does this indicate that Diet A is better than Diet B?

2. Random samples of 50 women and 50 men are taken at Norwich University. They are asked their reaction
to increased tuition fees. Of the women, 23 favored the increase. Of the men, 19 favor the increase. At a
10% significance level, does this indicate that a larger proportion of women favor the increase than men?

3. A method currently used by doctors to screen patients for a certain type of cancer fails to detect cancer in
15% of the patients who actually have the disease. A new method has been developed that researchers hope
will be able to detect cancer more accurately. A random sample of 80 patients known to this type of cancer
is screened using the new method and the method failed to detect the cancer in 8 patients. At the 5% level
of significance, can the researchers conclude that the new method is better than the one currently in use?
(Can they conclude that the new method fails to detect cancer in less than 15% of the patients who actually
have the disease?)

4. Beetles in oats. In a study of leaf beetle damage on oats, researchers measured the number of beetle larvae
per stem in small plots of oats after randomly applying one of two treatments: no pesticide or malathion at
the rate of 0.25 pound per acre. Below are the summary statistics. Compute a 95% confidence interval for
the difference in the mean number of beetle larvae per stem for the no pesticide group and malathion group.

Group Treatment Mean, St. Dev,  n
1 no pesticide        3.47, 1.21, 13
2 malathion           1.36, 0.52, 14

5. A coffee shop claims that its fresh-brewed drinks have a mean caffeine content of 80 milligrams per 5
ounces. A city health agency believes that the coffee shop’s fresh- brewed drinks have higher caffeine
content. To test this claim the health agency takes a random sample of 100 five-ounce servings and found
the average mean caffeine content of the sample was 87 milligrams with standard deviation of 25
milligrams. Does this provide enough evidence at the 1% significance level to claim that the coffee shop’s
fresh- brewed drinks have higher caffeine content? (Adapted from Reader’s Digest Eating for Good
Health.)
6. In a recent survey of county high school students, 100 males and 100 females, 66 of the male students and
47 of the female students sampled admitted that they consumed alcohol on a regular basis. Find a 90%
confidence interval for the difference between the proportion of male and female students that consume
alcohol on a regular basis. Can you draw any conclusions from the confidence interval?
7. Does using premium gas increase your miles per gallon? A study was conducted with nine vehicles that can
run on regular gas to see if using premium gas will get better gas mileage. Each car in our sample was
randomly filled first with either regular or premium gasoline, and the mileage for that tankful recorded. The
mileage was recorded again for the same cars for a tankful of the other kind of gasoline. Is there evidence to
suggest that using premium gas will increase your miles per gallon? (Use 10% significance level.)
Gas Mileage (mpg)
Vehicle 1: 19, 20, -1
Vehicle 2: 35, 32, 3
Vehicle 3: 34, 33, 1
Vehicle 4: 18, 19, -1
Vehicle 5: 40, 37, 3
Vehicle 6: 26, 27, -1
Vehicle 7: 36, 33, 3
Vehicle 8: 28, 29, -1
Vehicle 9: 34, 31, 3
Mean:      30, 29, 1
St Dev: 7.7, 6.1, 2.0

8. Suppose the mean salary for full professors in the United States is believed to be \$71,650. A sample of 15
full professors revealed a mean salary of \$74,250 with a standard deviation of \$5,000. Can it be concluded
that the average salary has increased using a 1% level of significance?

*****Notes to Tutor*****

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