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**Elementary Statistics Confidence Interval and Significance Test Problems for Means | Solution**

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**Elementary Statistics Confidence Interval and Significance Test Problems for Means**

Assignment Guidelines:

o Your work must be organized neatly and typed.

o Clearly indicate your name and the assignment number in the file name.

o Electronic copies of your work can be submitted as an attachment to the drop box.

o You need to hand in individual work. You may talk with each other about the problems. However, everything in the assignment must be your own work.

o No late assignments will be accepted.

The key steps to tests of significance are to state H0 and HA, calculate the test statistic, compute the p- value, and make a conclusion based on the given significance level. If you input H0, HA, and the summary statistics intoMinitab Express, Minitab Express will output the p-value and you will not have to make any complex calculations. Keep in mind that the results obtained from software are not meaningful unless the correct null and alternative hypotheses are determined.

Here is an example of what you will need to do for five of the six problems in this assignment: Testing the Population Mean You measure the weights of a random sample of 24 male runners 18 to 24 years old. The sample mean is 60kg and sample standard deviation is 5kg. A local gym advertises that the mean weight for this group of men is 62kg. Does this sample give enough evidence to suggest that the mean weight is actually less than the gym is advertising? (Use a 5% significance level.)

WORK YOU NEED TO SUBMIT:

Solution Question 1:

Step 1: H0: μ = 62

HA: μ < 62

Step 2: t = – 1.96

Step 3: p-value = 0.03114

Step 4: Reject H0 at the 5% level. There is enough evidence to suggest that the mean weight of male

runners 18 to 24 years old is actually less than the gym’s advertised value of 62kg.

If the question requires a test of significance, your solution should clearly show the four steps to the test. In addition, you should show that you have checked that the conditions for inference are met.

Step 1: State the null and alternative hypothesis. (Use “mu” for the symbol μ.)

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. The increasing cost of health care is an important issue today. Suppose that a random sample of 36 small companies that offer paid health insurance as a benefit was selected. The mean health insurance cost per worker per month was $124 with a standard deviation of $30. Construct a 95% confidence interval for the average health cost per worker per month for all small companies.

2. Suppose that the mean time to relief for a standard drug for treating migraines is 2.8 hours. A new drug is proposed to help treat migraines. In a controlled study, 100 patients who suffer from migraines are given the new drug upon the start of their next migraine attack and the mean time to relief was 2.63 hours with standard deviation of 0.9 hours. Does this indicate at the 1% significance level that the new drug reduces the mean time to relief for treating migraines?

3. Professor Handy measured the time in seconds required to catch a falling meter stick for 12 randomly selected students’ dominant hand and nondominant hand. Professor Handy claims that the reaction time in an individual’s dominant hand is less than the reaction time in their nondominant hand. Assuming that the differences follow a normal distribution, test the claim at the 5% significance level. Note: You do not need to type these values into Minitab Express, the data file has been created for you.

Student

Dominant

Hand

Nondominant

Hand

1 0.177 0.179

2 0.210 0.202

3 0.186 0.208

4 0.189 0.184

5 0.198 0.215

6 0.194 0.193

7 0.160 0.194

8 0.163 0.160

9 0.166 0.209

10 0.152 0.164

11 0.190 0.210

12 0.172 0.197

4. Suppose that two brands of gasoline were being compared for mileage. Samples of each brand were taken and used in identical cars under identical conditions. Nine tests were made of Band I and six tests of Brand II on large pick-up trucks. The following miles per gallon were found. Assuming the samples came from normally distributed, independent populations, are the two brands significantly different? (Use a 5% significance level.) Note: You do not need to type these values into Minitab Express, the data file has been created for you.

Brand I Brand II

16 13

18 15

15 11

23 17

17 12

14 13

19

21

16

5. Mary has developed a new way of teaching story problems in sixth grade arithmetic. She used her

method on a random sample of 50 sixth graders from her school. An independent random sample of 50 sixth graders was taught to solve story problems by a traditional method. All students were given the same test. Mary's students had an average score x1 = 82 (out of 100 possible points) with standard deviation s1 = 8.5. The other group had an average x2 = 75 with standard deviation s2 = 10.0. Does the new method improve performance on story problems? (Use a 5% significance level.)

6. A study was conducted to investigate the effectiveness of hypnotism in reducing pain. Results for

randomly selected subjects are given below. At the 5% level of significance, test the claim that the

sensory measurements are lower after hypnotism (scores are in cm. on a pain scale). Assume sensory measurements are normally distributed. Note: You do not need to type these values into Minitab Express, the data file has been created for you.

Before 6.6 6.5 9.0 10.3 11.3 8.1 6.3 11.6

After 6.8 2.4 7.4 8.5 8.1 6.1 3.4 2.0

**Prob3ProfHandys Data Solution included in .zip file****Prob4Gasoline Solution included in .zip file****Prob6HypnotismData Solution included in .zip file**

**Elementary Statistics Confidence Interval and Significance Test Problems for Means | Solution**

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