Fundamentals of Statistics (5th Edition)
5th Edition
ISBN: 9780134508306
Author: Michael Sullivan III
Publisher: PEARSON
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Chapter 12.1, Problem 8AYU
a.
To determine
The
χ 2
b.
To determine
The degrees of freedom.
c.
To determine
The critical value using
α = 0.05
d.
To determine
To test: The hypothesis at
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1. A sample of data is collected from a group of college students (X = 112, Sx = 12, N = 58). It is hypothesized that members of
this group have higher test scores than the general population (u = 100, o = 15). What test do you conduct? Don't do the test,
just name the test and list the relevant equation for the test statistic.
%3D
2. The critical value of t is 1.383, the value of the test statistic t = -1.383; therefore, we do not reject H0
a. True
b. False
6. Find p-value for testing Ho: ß1
= 0 and Ha: B1 # 0. Test hypothesis at a = .1,.05, and .01
7. Find p-value for testing Ho: ß2 = 0 and Ha: B2 # 0. Test hypothesis at a = .1,.05, and .01
%3D
Chapter 12 Solutions
Fundamentals of Statistics (5th Edition)
Ch. 12.1 - True or False: The shape of the chi-square...Ch. 12.1 - A _____ test is an inferential procedure used to...Ch. 12.1 - Suppose there are n independent trials of an...Ch. 12.1 - What are the two requirements that must be...Ch. 12.1 - In Problems 5 and 6, determine the expected counts...Ch. 12.1 - In Problems 5 and 6, determine the expected counts...Ch. 12.1 - Prob. 7AYUCh. 12.1 - Prob. 8AYUCh. 12.1 - In Problems 710, determine (a) the 2 test...Ch. 12.1 - In Problems 710, determine (a) the 2 test...
Ch. 12.1 - Applying the Concepts 11. NW Plain MMs According...Ch. 12.1 - Peanut MMs According to the manufacturer of MMs,...Ch. 12.1 - Prob. 13AYUCh. 12.1 - Prob. 14AYUCh. 12.1 - Always Wear a Helmet The National Highway Traffic...Ch. 12.1 - Religion in Congress Is the religious make-up of...Ch. 12.1 - Does It Matter Where I Sit? Does the location of...Ch. 12.1 - Racial Profiling On January 1, 2004, it became...Ch. 12.1 - Prob. 19AYUCh. 12.1 - Prob. 20AYUCh. 12.1 - Prob. 21AYUCh. 12.1 - Is the Die Loaded? A player in a craps game...Ch. 12.1 - Grade Distributions At Joliet Junior College, the...Ch. 12.1 - Population Shift An urban economist wonders if the...Ch. 12.1 - Prob. 25AYUCh. 12.1 - Living Alone? In 2000, 25.8% of Americans 15 years...Ch. 12.1 - Putting It Together: The V-2 Rocket in London In...Ch. 12.1 - Putting It Together: Weldons Dice On February 2,...Ch. 12.1 - Buying a New Car How much does the typical person...Ch. 12.1 - Why is goodness of fit a good choice for the title...Ch. 12.1 - Explain why chi-square goodness-of-fit tests are...Ch. 12.1 - Prob. 32AYUCh. 12.2 - True or False: The expected frequencies in a...Ch. 12.2 - In a chi-square test for ____ of proportions, we...Ch. 12.2 - The following table contains observed values and...Ch. 12.2 - The table in the next column contains observed...Ch. 12.2 - Prob. 5AYUCh. 12.2 - Prob. 6AYUCh. 12.2 - NW Family Structure and Sexual Activity A...Ch. 12.2 - Prenatal Care An obstetrician wants to learn...Ch. 12.2 - Health and Happiness Are health and happiness...Ch. 12.2 - Health and Education Does amount of education play...Ch. 12.2 - Social Well-Being and Obesity The Gallup...Ch. 12.2 - Profile of Smokers The following data represent...Ch. 12.2 - Efficacy of e-Cigs Do electronic cigarettes assist...Ch. 12.2 - Celebrex Celebrex, a drug manufactured by Pfizer,...Ch. 12.2 - NW Whats in a Word? In a recent survey conducted...Ch. 12.2 - Whats in a Word? Part II In a recent survey...Ch. 12.2 - Dropping a Course A survey was conducted at a...Ch. 12.2 - Prob. 18AYUCh. 12.2 - Prob. 19AYUCh. 12.2 - Prob. 20AYUCh. 12.2 - Putting It Together: Women, Aspirin, and Heart...Ch. 12.2 - Homeruns Go to...Ch. 12.2 - Explain the differences between the chi-square...Ch. 12.2 - Why does the test for homogeneity follow the same...Ch. 12.3 - Suppose a least-squares regression line is given...Ch. 12.3 - Prob. 2AYUCh. 12.3 - Prob. 3AYUCh. 12.3 - Prob. 4AYUCh. 12.3 - Prob. 5AYUCh. 12.3 - Prob. 6AYUCh. 12.3 - Prob. 7AYUCh. 12.3 - Prob. 8AYUCh. 12.3 - Prob. 9AYUCh. 12.3 - Prob. 10AYUCh. 12.3 - An Unhealthy Commute The following data represent...Ch. 12.3 - Credit Scores An economist wants to determine the...Ch. 12.3 - Height versus Head Circumference A pediatrician...Ch. 12.3 - Hurricanes The data in the next column represent...Ch. 12.3 - Concrete As concrete cures, it gains strength. The...Ch. 12.3 - Tar and Nicotine Every year the Federal Trade...Ch. 12.3 - Invest in Education Go to...Ch. 12.3 - American Black Bears In 1969, Dr. Michael R....Ch. 12.3 - CEO Performance (Refer to Problem 31 in Section...Ch. 12.3 - Bear Markets (Refer to Problem 32. Section 4.1) A...Ch. 12.3 - Age versus HDL Cholesterol A doctor wanted to...Ch. 12.3 - Prob. 22AYUCh. 12.3 - Influential Observations Zillow.com is a site that...Ch. 12.3 - Why is it important to perform graphical as well...Ch. 12.3 - Prob. 25AYUCh. 12.3 - Why is it desirable to have the explanatory...Ch. 12.4 - Intervals constructed about the predicted value of...Ch. 12.4 - Prob. 2AYUCh. 12.4 - Prob. 3AYUCh. 12.4 - Using the sample data from Problem 6 in Section...Ch. 12.4 - Prob. 5AYUCh. 12.4 - Prob. 6AYUCh. 12.4 - Prob. 7AYUCh. 12.4 - Prob. 8AYUCh. 12.4 - Prob. 9AYUCh. 12.4 - Prob. 10AYUCh. 12.4 - Prob. 11AYUCh. 12.4 - Tar and Nicotine Use the results of Problem 16 in...Ch. 12.4 - Prob. 13AYUCh. 12.4 - Prob. 14AYUCh. 12.4 - CEO Performance Use the results of Problem 19 from...Ch. 12.4 - Prob. 16AYUCh. 12.4 - Prob. 17AYUCh. 12 - Roulette Wheel A pit boss suspects that a roulette...Ch. 12 - Prob. 2RECh. 12 - Titanic With 20% of men, 74% of women, and 52% of...Ch. 12 - Prob. 4RECh. 12 - Prob. 5RECh. 12 - Prob. 6RECh. 12 - Seat Choice and GPA A biology professor wants to...Ch. 12 - Apartments The following data represent the square...Ch. 12 - Calories versus Sugar The following data represent...Ch. 12 - A pit boss is concerned that a pair of dice being...Ch. 12 - Prob. 2CTCh. 12 - The Harris Poll asked a random sample of adult...Ch. 12 - Prob. 4CTCh. 12 - Prob. 5CTCh. 12 - Prob. 6CTCh. 12 - Crickets make a chirping noise by sliding their...Ch. 12 - The following data represent the height (inches)...Ch. 12 - A researcher believes that as age increases, the...Ch. 12 - CASE STUDY Feeling Lucky? Well, Are You? In fiscal...
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- 2) Suppose that we are testing Ho:µ = 4 vs Ha: µ > 4. A p-value of 0.023 was determined. Which of the following is a correct interpretation of this p-value? (a) The null hypothesis would be rejected at a 5% level but not a 1% level. (b) The null hypothesis would be rejected at a 1% level but not a 5% level. (c) The null hypothesis would be rejected at both 5% and 1% levels. (d) The null hypothesis would not be rejected at either the 5% or 1% level.arrow_forward1. You are performing a two-tailed test with a sample size of 44.If α=.02α=.02, find the positive critical value, to four decimal places.tα/2= ? 2. You are performing a two-tailed test with a sample size of 88.If α=.01α=.01, find the positive critical value, to four decimal places.tα/2= ?arrow_forward3. For the data in the source table, what decision can be made about the hypotheses being tested? Source df F 2 4 Between-groups Subjects Within-groups Total O SS 10.1 7.4 8.5 26 d. 8 14 Oa. Fail to reject the null hypothesis and conclude that there is no effect of the independent variable. Ob. Fail to reject the null hypothesis because the F statistic does not exceed the critical cutoff. Oc. Reject the null hypothesis and conclude that the independent variable has no effect. MS 5.05 1.85 1.063 Reject the null hypothesis and conclude that there are differences among the levels of the independent variable.arrow_forward
- If, in a sample of n=20 selected from a normal population, X = 54 and S = 12, what is your statistical decision if the level of significance, a is 0.01, the null hypothesis, Ho. is i = 50, and the alternative hypothesis, H, is #502 Click here to view page 1 of the table of the critical values of t. Click here to view page 2 of the table of the critical values oft. Determine the critical value(s). The critical value(s) is(are)| (Round to four decimal places as needed. Use a comma to separate answers as needed.)arrow_forward3. Suppose you are testing Ho: µ = 62 H1: µ + 62 versus where o? is unknown and n = 14. The data come from a normal population. From your data, you calculate your test statistic value as -2.483. (a) Should you use z or t when finding a p-value for this scenario? (b) Calculate the p-value for this scenario. (c) What is the smallest level of significance (a value) such that we Reject Ho in this scenario?arrow_forward6. For a left-tailed test when n = 8 and a = 0.10 the critical value is %3D a. 1.397 b. -1.397 C. 1.415 d. -1.415arrow_forward
- 6. Show that 1 s2 E1(Xi – x)² is unbiased estimator of the population variance o? i=1 п-1arrow_forward4. The amount of contaminants in two independent samples (comprised of independent subjects) from two distinct bird species is measured in a veterinary hospital. The summary of the data is presented below. Data from Pop. 1 Data from Pop. 2 n1=13 71=1.12 $1=0.52 72=D15 I2=1.49 S2=0.70 We are interesting in testing Ho: -P2=0, versus H,: A-A20. And we will mnake the normality assumption. (a) Suppose that we know the population variances: of = 0.1, o = 0.2. Design the test and find its pvalue. What conclusion do you reach at significance level 5%? (b) Suppose that the researchers do not trust these population vari- ance values, and would like to do the test based on the sample variances provided above. Assuming equal variance, how would your conclusions changed? %3Darrow_forward16% of all Americans suffer from sleep apnea. A researcher suspects that a lower percentage of those who live in the inner city have sleep apnea. Of the 398 people from the inner city surveyed, 52 of them suffered from sleep apnea. What can be concluded at the level of significance of αα = 0.01? For this study, we should use Z TEST FOR A POPULATION PROPORTION The null and alternative hypotheses would be: Ho: P=0.15 (please enter a decimal) H1: P <0.1 3. The test statistic _z__ = _______ (please show your answer to 3 decimal places.) 4. The p-value = __0.0144__ (Please show your answer to 4 decimal places.) 5. The p-value is __<__α 6. Based on this, we should ___FAIL TO REJECT___ the null hypothesis. Thus, the final conclusion is that ... The data suggest the populaton proportion is significantly smaller than 16% at αα = 0.01, so there is sufficient evidence to conclude that the population proportion of inner city residents who have sleep apnea is…arrow_forward
- If, in a sample of n=30 selected from a normal population, X=58 and S=12, what is your statistical decision if the level of significance, α, is 0.05, the null hypothesis, H0, is μ=50, and the alternative hypothesis, H1, is μ≠50? Click here to view page 1 of the table of the critical values of t. LOADING... Click here to view page 2 of the table of the critical values of t. LOADING... Question content area bottom Part 1 Determine the critical value(s). The critical value(s) is(are) enter your response here.arrow_forwardD please You are testing the null hypothesis that there is no linear relationship between two variables, X and Y. From your sample of n=18, you determine that b1=4.1 and Sb1=1.1. a. What is the value of tSTAT? b. At the α=0.05 level of significance, what are the critical values? c. Based on your answers to (a) and (b), what statistical decision should you make? d. Construct a 95% confidence interval estimate of the population slope, β1. a. What are the hypotheses to test? A. H0: β1≤0 H1: β1>0 B. H0: β1=0 H1: β1≠0 This is the correct answer. C. H0: β1≠0 H1: β1=0 Your answer is not correct. D. H0: β1≥0 H1: β1<0 tSTAT=3.733.73 (Round to two decimal places as needed.) b. The lower critical value is negative 2.1199−2.1199. The upper critical value is 2.11992.1199. (Round to four decimal places as needed.) c. What statistical decision should you make? A. Since tSTAT is between the two…arrow_forward2. Participants were kept awake for a certain number of hours before given a visuospatial task. Researchers measured how many correct responses each participant had. Results are shown below. Use alpha = .01. Number of Correct Hours Kept Awake (X) Responses (Y) 21 X = 10 SS, = 422 SPy= -525 S, -5.70 2 Y = 10 4 19 SS, = 690 13 ху 20 S, = 7.29 9. 11 10 5 5 14 15 17 2 18 1 17 1 13 4 2 18 8 11arrow_forward
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