# Final Exam MATH 221

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**Final Exam MATH 221**

The table below shows the number of male and female students enrolled in nursing…

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## Final Exam MATH 221

Final Exam MATH 221

**A+ Formulas in Excel and in Word are included**

- The table below shows the number of male and female students enrolled in nursing at a university for a certain semester. A student is selected at random. Complete parts (a) through (d) (a)Find the probability that the student is male or a nursing major.

P (being male or being nursing major) =

(b) Find the probability that the student is female or not a nursing major.

P(being female or not being a nursing major) =

(c) Find the probability that the student is not female or a nursing major

P(not being female or not being a nursing major) =

(d) Are the events “being male” and “being a nursing major” mutually exclusive? Explain.

- An employment information service claims the mean annual pay for full-time male workers over age 25 without a high school diploma is $22,325. The annual pay for a random sample of 10 full-time male workers over age 25 without a high school diploma is listed. At a = 0.10, test the claim that the mean salary is $22,325. Assume the population is normally distributed.

20,660 – 21,134 – 22,359 – 21,398 – 22,974, – 16,919 – 19,152 – 23,193 – 24,181 – 26,281

(a) Write the claim mathematically and identify

Which of the following correctly states ?

Final Exam MATH 221

(b) Find the critical value(s) and identify the rejection region(s).

What are the critical values?

Which of the following graphs best depicts the rejection region for this problem?

(c) Find the standardized test statistics.

t =

(d) Decide whether to reject or fail to reject the null hypothesis.

reject because the test statistics is in the rejection region.

a. fail to reject because the test statistic is not in the rejection region.

c. reject because the test statistic is not in the rejection region.

d. fail to reject because the test statistic is in the rejection region.

Final Exam MATH 221

(e) Interpret the decision in the context of the original claim.

a. there is sufficient evidence to reject the claim that the mean salary is $22,325.

b. there is not sufficient evidence to reject the claim that the mean salary is not $22,325.

c. there is sufficient evidence to reject the claim that the mean salary is not $22,325.

d. there is not sufficient evidence to reject the claim that the mean salary is $22,325.

- The times per week a student uses a lab computer are normally distributed, with a mean of 6.1 hours and a standard deviation of 1.2 hours. A student is randomly selected. Find the following probabilities.

(a) The probability that the student uses a lab computer less than 5hrs a week.

(b) The probability that the student uses a lab computer between 6-8 hrs a week.

(c) The probability that the student uses a lab computer for more than 9 hrs a week.

(a) =

(b) =

(c) =

- Write the null and alternative hypotheses. Identify which is the claim.

A study claims that the mean survival time for certain cancer patients treated immediately with chemo and radiation is 13 months. - Find the indicated probability using the standard normal distribution.

P(z>) = - The Gallup Organization contacts 1323 men who are 40-60 years of age and live in the US and asks whether or not they have seen their family doctor.What is the population in the study?

Answer:What is the sample in the study?

Answer:

Final Exam MATH 221

- The ages of 10 brides at their first marriage are given below.

4 32.2 33.6 41.2 43.4 37.1 22.7 29.9 30.6 30.8(a) find the range of the data set.

Range =

(b) change 43.4 to 58.6 and find the range of the new date set.

Range =

(c) compare your answer to part (a) with your answer to part (b)

- The following appear on a physician’s intake form. Identify the level of measurement of the data.

(a) Martial Status

(b) Pain Level (0-10)

(c) Year of Birth

(d) Height(a) what is the level of measurement for marital status(b) what is the level of measurement for pain level(c) what is the level of measurement for year of birthWhat is the level of measurement for height

- To determine her air quality, Miranda divides up her day into 3 parts; morning, afternoon, and evening. She then measures her air quality at 3 randomly selected times during each part of the day. What type of sampling is used?

- Find the equation of the regression line for the given data. Then construct a scatter plot of the data and draw the regression line. Then use the regression equation to predict the value of y for each of the given x-values, if meaningful. The caloric content and the sodium content (in milligrams) for 6 beef hot dogs are shown in the table below.

- X= 150 calories
- X= 100 calories
- X = 120 calories
- X = 60 calories

Final Exam MATH 221

Find the regression equation.

=

Choose the correct graph below.

(a) predict the value of y for x = 150.

Answer:

(b) predict the value of y for x = 100.

Answer:

(c) predict the value of y for x = 120.

Answer:

(d) predict the value of y for x = 60.

Answer:

11. A restaurant association says the typical household spends a mean of $4072 per year on food away from home. You are a consumer reporter for a national publication and want to test this claim. You randomly select 12 households and find out how much each spent on food away from home per year. Can you reject the restaurant association’s claim at a = 0.10? Complete parts a through d.

- Write the claim mathematically and identify. Choose the correct the answer below.

Use technology to find the P-value.

P =

Decide whether to reject or fail the null hypothesis.

Interpret the decision in the context of the original claim. Assume the population is normally distributed. Choose the correct answer below.

12. The table below shows the results of a survey in which 147 families were asked if they own a computer and if they will be taking a summer vacation this year.

Final Exam MATH 221

(a) find the probability that a randomly selected family is not taking a summer vacation year.

Probability =

(b) find the probability that a randomly selected family owns a computer

Probability =

(c) find the probability that a randomly selected family is taking a summer vacation this year and owns a computer

Probability =

(d) find the probability a randomly selected family is taking a summer vacation this year and owns a computer.

Probability =

- Are the events of owning a computer and taking a summer vacation this year independent or dependent events?
- 13. Assume the Poisson distribution applies. Use the given mean to find the indicated probability.

Find P(5) when ᶙ = 4

P(5) =

14. In a survey of 7000 women, 4431 say they change their nail polish once a week. Construct a 99% confidence interval for the population proportion of women who change their nail polish once a week.

A 99% confidence interval for the population proportion is…

15 A random sample of 53 200-meter swims has a mean time of 3.32 minutes and the population standard deviation is 0.06 minutes. Construct a 90% confidence interval for the population mean time. Interpret the results.

The 90% confidence interval is

Interpret these results. Choose the correct answer:

Answer: With 90% confidence, it can be said that the population mean time is between the end points of the given confidence interval.

16. Determine whether the variable is qualitative or quantitative: Weight

Quantitative

Qualitative

17. 32% of college students say that they use credit cards because of the reward program. You randomly select 10 college students and ask each to name the reason he or she uses credit cards. Find the probability that the number of college students who say they use credit cards because of the reward program is (a) exactly two, (b), more than two, and (c), between two and five inclusive.

(a) P(2) =

(b) P(X>2) =

(c) P(2__<__x__<__5) =

Final Exam MATH 221

18. A light bulb manufacturer guarantees that the mean life of a certain type of light bulb is at least 950 hours. A random sample of 74 light bulbs has a mean life of 943 hours with a standard deviation of 90 hours. Do you have enough evidence to reject the manufacturer’s claim? Use ᶏ = 0.04

- Identify the critical value(s).(c) identify the standardized test statistic.

z =

(d) decide whether to reject or fail to reject the null hypothesis.A. Reject . There is sufficient evidence to reject the claim that the bulb life is at least 950 hours.

B. Fail to reject . There is not sufficient evidence to reject the claim that the mean bulb life is at least 950 hours.

C. Fail to reject . There is sufficient evidence to reject the claim that mean bulb life is at least 950 hours.

D. Reject . There is not sufficient evidence to reject the claim that mean bulb life is at least 950 hours.19. Use technology to find the sample size, mean, medium, minimum data value, and maximum data value of the data. The data represents the amount (in dollars) made by several families during a community yard sale.

25 67.25 156 134.75 98.25 149.25 124.75 109.75 117 104.75 76The sample size is

The mean is

The medium is

The minimum data value is

The maximum data value is20. A researcher wishes to estimate, with 95% confidence, the proportion of adults who have high-speed internet access. Her estimate must be accurate within 5% of the true proportion.

(a) find the minimum sample size needed, using a prior study that found 54% of the respondents said they have high-speed internet access.

(b) no preliminary estimate is available. Find the minimum sample size needed.(a) what is the minimum sample size needed using a prior study that found that 54% of the respondents said they have high-speed internet access?n =(b) what is the minimum sample size needed assuming that no preliminary estimate is available?n =21. You interview a random sample of 50 adults. The results of the survey show that 50% of the adults said they were more likely to buy a product where there are free samples. At ᶏ = 0.05, can you reject the claim that at least 54% of the adults are more likely to buy a product when there are free samples?State the null and alternative hypotheses. Choose the correct answer below.

Determine the critical value(s).

The critical value(s) is/are

find the z-test statistic.

z =

what is the result of the test?

A. reject . The data provide sufficient evidence to reject the claim.

- fail to reject . The data provide sufficient evidence to reject the claim.

C. Reject . The data do not provide sufficient evidence to reject the claim.

D. fail to reject . The data do not provide sufficient evidence to reject the claim.

22. The budget (in millions of dollars) and worldwide gross (in millions of dollars) for eight movies are shown below. Complete parts (a) through (c)

Final Exam MATH 221

Budget X | 209 | 203 | 198 | 198 | 179 | 176 | 175 | 168 |

Gross Y | 254 | 341 | 453 | 656 | 721 | 1049 | 1839 | 1267 |

(a) display the data in a scatter plot. Choose the correct graph below.

(b) calculate the correlation coefficient r.

r =

(c) make a conclusion about the type of correlation.

The correlation is a …linear correlation.

23. A machine cuts plastic into sheets that are 30 feet (360 inches) long. Assume that the population of lengths is normally distributed. Complete parts a and b.

- The company wants to estimate the mean length the machine is cutting the plastic within 0.125 inch. Determine the minimum sample size required to construct a 95% confidence interval for the population mean. Assume the population standard deviation is 0.25 inch.

n =

Repeat part (a) using an error tolerance of 0.0625 inch.

n =

Which error tolerance requires a larger sample size? Explain.

- The tolerance E = 0.0625 inch requires a larger sample size. As error size decreases, a larger sample must be taken to ensure the desired accuracy.
- The tolerance E = 0.125 inch requires a larger sample size. As error size decreases, a larger sample must be taken to ensure the desired accuracy.
- The tolerance E = 0.125 inch requires a larger sample size. As error size increases, a larger sample must be taken to ensure the desired accuracy.
- The tolerance E = 0.0.625 inch requires a larger sample size. As error size increases, a larger sample must be taken to ensure the desired accuracy.

MATH221 Final Exam Statistics

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