Elementary Statistics Final

Chapter 7-10 practice problems

Essentials of Statistics, Triola

(spring 06 ) 1) When people smoke, the nicotine they absorb is converted to cotinine, which can be

measured. A sample of 40 smokers has a mean cotinine level of 172.5 and a standard deviation of 109.5. Assuming the levels of cotinine are normally distributed, construct a 95% confidence interval estimate for the population mean of the cotinine level of all smokers.

(Round your answer to the thousandths place.) 2) DETERMINING SAMPLE SIZE: “An economist wants to estimate the mean income

for the first year of work for college graduates who have taken a statistics course. How many such incomes must be found if we want to be 99% confident that the sample mean is within $400 of the true population mean? (This means that the margin of error is 400) Assume that a previous study has revealed that for such incomes σ = $6250 (Round Z to the thousandths place)

( Round your final answer by using the round off rule for Sample Sizes)

A researcher wishes to determine whether the salaries of professional nurses employed by private hospitals are higher than those of nurses employed by government-owned hospitals. She selects a sample of nurses from each type of hospital and calculates the means and standard deviations of their salaries. private:

n1 = 32, x1 =$26,800, s1 = $600

government:

n2 = 40, x2 =$25, 400, s2 = $450

3) Construct a 95% confidence interval for the difference between the two population

means . 4) Is there a significant difference between the two groups? Does one hospital really

pay more than the other? Explain your answer by using the confidence interval from above.

A random sample of 100 babies is obtained, and the mean head circumference is found to be 40.6 cm. Assuming that the population standard deviation is known to be 1.6 cm, ( that means that σ =1.6) use a 0.05 significance level to test the claim that the mean head circumference is equal to 40.0 cm. 5) Which parameter is being tested here? a) µ b) σ c) Ρ 6) Where does the claim go? H_0 or H_1 7) The null hypothesis is _____________ 8) The alternate hypothesis is ______________ 9) The test statistic is 10) The critical value is 11) The p-value is 12) Which is the correct conclusion for the problem. _________ a) The sample data support the claim that the mean head circumference is equal to 40.0 cm. b) There is not sufficient sample evidence to support the claim that the mean head circumference is equal to 40.0 cm. c) There is sufficient evidence to warrant rejection of the claim that the mean head circumference is equal to 40.0 cm. d) There is not sufficient evidence to warrant rejection of the claim that the mean head circumference is equal to 40.0 cm.

With multiple lines for its various windows, the Jefferson Valley Bank found that the standard deviation for normally distributed waiting times on Friday afternoons was 6.2 min. The bank experimented with a single main waiting line and found that for a simple random sample of 25 customers, the waiting times have a standard deviation of 3.8 min. Use a significance level of 0.05 to test the claim that a single line causes lower variation among the waiting times. In other words, Test that a single line results in a lower variation of waiting times when compared to multiple lines (σ < 6.2) 13) What is the null hypothesis? ____________ 14) What is the alternate hypothesis?____________ 15) Find the test statistic 16) The critical value is 17) Which is the correct conclusion for the problem. _________ a) The sample data support the claim that a single line causes lower variation among the

waiting times. b) There is not sufficient sample evidence to support the claim that a single line causes lower

variation among the waiting times. c) There is sufficient evidence to warrant rejection of the claim that a single line causes lower

variation among the waiting times. d) There is not sufficient evidence to warrant rejection of the claim that a single line causes

lower variation among the waiting times.

A local elementary school claims that its new tutoring program helps students raise their scores on math tests. The table shows the scores of 6 students before the implementation of this new tutoring program and the scores after the implementation of the new tutoring program. At a 0.10 significance level, can you conclude that the tutoring program helps students raise their math test scores? Test the claim that the tutoring program helps students get better scores on their math tests. Before program

80 75 30 68 81 78

After program

80 80 70 75 95 75

18) Which statement represents the claim? Circle your choice below.

) 0 ) 0 ) 0 ) 0d d d da U b U c U d U= > < ! ,

1 2 1 2 1 2 1 2) ) ) )e U U f U U g U U h U U= > < ! 19) The null hypothesis is _____________ 20) The alternate hypothesis is ______________ 21) The test statistic is _______________ 22) The critical value is _______________ 23) The p-value is ______________ 24) Choose one. a) FAIL TO REJECT 0H b) REJECT 0H . 25) Is this particular tutoring program effective in helping students raise their math test scores ?

When nicotine is absorbed by the body, cotinine is produced. A measurement of cotinine in the body is therefore a good indicator of how much a person smokes. Listed below are the reported numbers of cigarettes smoked per day and the measured amounts of nicotine ( in ng/mL) X Cigarettes smoked per day

10 15 20 2 7 4

Y Cotinine level

283 174 350 1.85 43.4 75.6

Round to the thousandths place 26) Find the value of the linear correlation coefficient (r) 27) Is there a significant linear correlation? ( This is not just a “yes” or “no” question,

show all steps in a hypothesis test leading to your answer) 28) If a significant linear correlation exists, find the regression equation. If there is no

significant linear correlation, find y . 29) Find the best predicted cotinine level if a person smokes 8 cigarettes per day.

A medical researcher claims that less than 23% of U.S. adults are smokers. In a random sample of 200 adults, 22.5% say that they are smokers. Test the claim that the proportion of adults who smoke is less than 23%. Use a significance level of .10 30) The null hypothesis is _____________ 31) The alternate hypothesis is ______________ 32) The test statistic is _______________ 33) The critical value is _______________ 34) The p-value is ______________ 35) Choose one. a) FAIL TO REJECT 0H b) REJECT 0H . 36) What is your conclusion? Write it out using the “wording of final conclusion” table.