MAT 130: Beginning Statistics

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Allied American University

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This paper was prepared for [INSERT COURSE NAME], [INSERT COURSE ASSIGNMENT] taught by [INSERT INSTRUCTOR’S NAME].

PART I: SHORT RESPONSE

Directions: Please answer each of the following questions thoroughly.

1. Bottles of Bayer aspirin are labeled with a statement that the tablets each contain 325 mg of aspirin. A quality control manager claims that a large sample of data can be used to support the claim that the mean amount of aspirin in the tablets is equal to 325 mg, as the label indicates. Can a hypothesis test be used to support that claim? If so, identify the null and alternative hypotheses.

2. Make a decision about the given claims. Use only the rare event rule stated in Section 8-2, and make subjective estimates to determine whether events are likely. For example, if the claim is that a coin favors heads and sample results consist of 11 heads in 20 flips, conclude that there is not sufficient evidence to support the claim that the coin favors heads (because it is easy to get 11 heads in 20 flips by chance with a fair coin).

a. Claim: A coin favors heads when tossed, and there are 90 heads in 100 tosses.

b. Claim: Movie patrons have IQ scores with a standard deviation that is less than the standard deviation of 15 for the general population. A simple random sample of 40 movie patrons results in IQ scores with a standard deviation of 14.8.

3. Examine the given statements then express the null hypothesis and alternative hypothesis in symbolic form. Be sure to use the correct symbol (μ , p, σ) for the indicated parameter.

a. The majority of college students have credit cards.

b. The proportion of homes with fire extinguishers is 0.80.

4. In preliminary results from couples using the Gender Choice method of gender selection to increase the likelihood of having a baby girl, 20 couples used the Gender Choice method with the result that 8 of them had baby girls and 12 had baby boys. Given that the sample proportion is 8/20 or 0.4, can the sample data support the claim that the proportion of girls is greater than 0.5? Can any sample proportion less than 0.5 be used to support a claim that the population proportion is greater than 0.5? Explain why or why not.

5. Test the given claim: In a presidential election, 308 out of 611 voters surveyed said that they voted for the candidate who won (based on data from ICR Survey Research Group). Use a 0.01 significance level to test the claim that among all voters, the percentage who believe that they voted for the winning candidate is equal to 43%, which is the actual percentage of votes for the winning candidate. What does the result suggest about voter perceptions?

a. Identify the null hypothesis.

b. Identify the alternative hypothesis.

c. Identify the test statistic, P-value or critical value(s).

d. Identify the conclusion about the null hypothesis and final conclusion that addresses the original claim. Use the P-value method. Use the normal distribution as an approximation to the binomial distribution (as described in Part 1 of section 8-3).

6. When testing a claim about a population mean with σ known, either or both of these conditions is satisfied: The population is normally distributed or the sample size n is greater than 30, that is, n > 30. How do we verify that a population is normally distributed?

7. In statistics, what does df denote? If a simple random sample of 20 speeds of cars on California Highway 405 is to be used to test the claim that the sample values are from a population with a mean greater than the posted speed limit of 65 mi h, what is the specific value of df?

8. What is a t test? Why is the letter t used?

9. Determine whether the hypothesis test involves a sampling distribution of means that is a normal distribution, Student t distribution, or neither. You may use Figure 7-6 and Table 7-1 in your textbook. Claim about daily rainfall amounts in Boston: μ < 0.20 in. Sample data: n = 52, = 0.10 in., s = 0.25 in. The sample data appear to come from a population with a distribution that is very far from normal, and is known.

10. Hypothesis tests of claims about the population mean or population standard deviation both require a simple random sample from a normally distributed population. How does the normality requirement for a hypothesis test of a claim about a standard deviation differ from the normality requirement for a hypothesis test of a claim about a mean?

11. Find the number of successes x suggested by the given statements:

a. From an article in Journal of the American Medical Association: Among 8834 malfunctioning pacemakers, in 15.8% the malfunctions were due to batteries.

b. From Pfizer: Among 129 subjects who took Chantix as an aid to stop smoking, 12.4% experienced nausea.

12. Assume that you plan to use a significance level of = 0.05 to test the claim that P1 = P2. Use the given sample sizes and numbers of successes below to find:

a. the pooled estimate ,

b. the z test statistic,

c. the critical z values,

d. the P-value.

Chantix is a drug used as an aid to stop smoking. The numbers of subjects experiencing insomnia for each of two treatment groups in a clinical trial of the drug Chantix are given below (based on data from Pfizer):

13. Assume that you want to use a 0.01 significance level to test the claim that the mean pulse rate of men is less than the mean pulse rate of women. What confidence level should be used if you want to test that claim using a confidence interval?

14. A nutritionist selects a simple random sample of 50 cans of Coke and another simple random sample of 50 cans of Pepsi. The cans are arranged as 50 pairs, then the sugar content of each can is measured. Are the two samples (Coke and Pepsi) independent or dependent? Explain.

15. When testing the claim that two different simple random samples heights of men are from populations having the same standard deviation, the author obtained the F test statistic of 1.010 (based on data from the National Health and Nutrition Examination Survey). What does the value of the F test statistic reveal about the sample data?

PART II: PROJECT

For this Module 5 Homework Assignment, please submit your response to the following:

Document your progress. Who did you interview? How many people did you interview? If you collected data, please submit it below. If not, please explain what you did to contribute to this assignment this past week.

Directions: This assignment is a course-long project whereby you will work on the project in each module. You will turn in your completed project at the end of Module 8.

Create a survey question to ask others. The following are examples or some survey questions:

1. Choose a random number between 1 and 10 inclusive.

2. What month of the year does your birthday fall on? Write the numeric value from 1 to 12.

3. How many keys are in your possession at this time?

4. How many siblings do you have?

In Module 1, you will submit your survey question to your instructor for approval. Once you are notified of its approval, you may begin conducting a survey using your question.

You will need at least 25 participants and will need to keep the following record for each person:

a. Gender

b. Age

c. Date surveyed

d. Survey response

Please also keep a count, if any, non-willing participants. For example, if you chose the first survey question, then you might have the following records:

In the Module 8 Homework Assignment, you will be asked to analyze your survey results, so please be sure to begin conducting your survey as soon as your question is approved. Try getting 5 participants a week to satisfy the required number of participants.