Researchers gave 40 index cards to a waitress at an Italian restaurant in New Jersey. Before delivering the bill to each customer, the waitress randomly selected a card and wrote on the bill the same message that was printed on the index card. Twenty of the cards had the message "The weather is supposed to be really good tomorrow. I hope you enjoy the day!" Another 20 cards contained the message "The weather is supposed to be not so good tomorrow. I hope you enjoy the day anyway!"
After the customers left, the waitress recorded the amount of the tip, percent of bill, before taxes. Given are the tips for those receiving the good‑weather message.
20.8  18.7  19.9  20.6  21.9  23.4  22.8  24.9  22.2  20.3 
24.9  22.3  27.0  20.5  22.2  24.0  21.2  22.1  22.0  22.7 
Given are the tips for the 20 customers who received the bad‑weather message.
18.0  19.1  19.2  18.8  18.4  19.0  18.5  16.1  16.8  14.0 
17.0  13.6  17.5  20.0  20.2  18.8  18.0  23.2  18.2  19.4 
Stemplots for both data sets are shown.
18  7 
19  9 
20  3 5 6 8 
21  2 9 
22  0 1 2 2 3 7 8 
23  4 
24  0 9 9 
25  
26  
27  0 
13  6 
14  0 
15  
16  1 8 
17  0 5 
18  0 0 2 4 5 8 8 
19  0 1 2 4 
20  0 2 
21  
22  
23  2 
Neither stemplot suggests a strong skew or the presence of strong outliers. Because of this, t procedures are reasonable here.
Is there good evidence that the two different messages produce different percent tips?
Let μ1 be the mean tip percent when the forecast is good, and let μ2 be the mean tip percent when the forecast is bad. Select the correct hypotheses statements that we want to test.
H0:μ1=μ2 versus Ha:μ1>μ2
H0:μ1=μ2 versus Ha:μ1≠μ2
H0:μ1=μ2 versus Ha:μ1<μ2
H0:μ1≠μ2 versus Ha:μ1<μ2
What degrees of freedom (df) would you use in the conservative two‑sample t procedures to compare the percentage of tips when the forecast is good and bad? (Enter your answer as a whole number.)
df=
What is the two‑sample t test statistic (rounded to three decimal places)?
t=
Test whether there is good evidence that the two different messages produce different percent tips at α=0.1 . The null hypothesis of no difference in tips due to the weather "forecast" is
not rejected.
rejected.
In: Math
The following data represent crime rates per 1000 population for a random sample of 46 Denver neighborhoods.†
63.2  36.3  26.2  53.2  65.3  32.0  65.0 
66.3  68.9  35.2  25.1  32.5  54.0  42.4 
77.5  123.2  66.3  92.7  56.9  77.1  27.5 
69.2  73.8  71.5  58.5  67.2  78.6  33.2 
74.9  45.1  132.1  104.7  63.2  59.6  75.7 
39.2  69.9  87.5  56.0  154.2  85.5  77.5 
84.7  24.2  37.5  41.1 
(a) Use a calculator with mean and sample standard deviation keys to find the sample mean x and sample standard deviation s. (Round your answers to one decimal place.)
x =  crimes per 1000 people 
s =  crimes per 1000 people 
(b) Let us say the preceding data are representative of the
population crime rates in Denver neighborhoods. Compute an 80%
confidence interval for μ, the population mean crime rate
for all Denver neighborhoods. (Round your answers to one decimal
place.)
lower limit  crimes per 1000 people 
upper limit  crimes per 1000 people 
(c) Suppose you are advising the police department about police
patrol assignments. One neighborhood has a crime rate of 61 crimes
per 1000 population. Do you think that this rate is below the
average population crime rate and that fewer patrols could safely
be assigned to this neighborhood? Use the confidence interval to
justify your answer.
Yes. The confidence interval indicates that this crime rate is below the average population crime rate.
Yes. The confidence interval indicates that this crime rate does not differ from the average population crime rate.
No. The confidence interval indicates that this crime rate is below the average population crime rate.
No. The confidence interval indicates that this crime rate does not differ from the average population crime rate.
(d) Another neighborhood has a crime rate of 75 crimes per 1000
population. Does this crime rate seem to be higher than the
population average? Would you recommend assigning more patrols to
this neighborhood? Use the confidence interval to justify your
answer.
Yes. The confidence interval indicates that this crime rate does not differ from the average population crime rate.
Yes. The confidence interval indicates that this crime rate is higher than the average population crime rate.
No. The confidence interval indicates that this crime rate is higher than the average population crime rate.
No. The confidence interval indicates that this crime rate does not differ from the average population crime rate.
(e) Compute a 95% confidence interval for μ, the
population mean crime rate for all Denver neighborhoods. (Round
your answers to one decimal place.)
lower limit  crimes per 1000 people 
upper limit  crimes per 1000 people 
(f) Suppose you are advising the police department about police
patrol assignments. One neighborhood has a crime rate of 61 crimes
per 1000 population. Do you think that this rate is below the
average population crime rate and that fewer patrols could safely
be assigned to this neighborhood? Use the confidence interval to
justify your answer.
Yes. The confidence interval indicates that this crime rate is below the average population crime rate.
Yes. The confidence interval indicates that this crime rate does not differ from the average population crime rate.
No. The confidence interval indicates that this crime rate is below the average population crime rate.
No. The confidence interval indicates that this crime rate does not differ from the average population crime rate.
(g) Another neighborhood has a crime rate of 75 crimes per 1000
population. Does this crime rate seem to be higher than the
population average? Would you recommend assigning more patrols to
this neighborhood? Use the confidence interval to justify your
answer.
Yes. The confidence interval indicates that this crime rate does not differ from the average population crime rate.
Yes. The confidence interval indicates that this crime rate is higher than the average population crime rate.
No. The confidence interval indicates that this crime rate is higher than the average population crime rate.
No. The confidence interval indicates that this crime rate does not differ from the average population crime rate.
(h) In previous problems, we assumed the x distribution
was normal or approximately normal. Do we need to make such an
assumption in this problem? Why or why not? Hint: Use the
central limit theorem.
Yes. According to the central limit theorem, when n ≥ 30, the x distribution is approximately normal.
Yes. According to the central limit theorem, when n ≤ 30, the x distribution is approximately normal.
No. According to the central limit theorem, when n ≥ 30, the x distribution is approximately normal.
No. According to the central limit theorem, when n ≤ 30, the x distribution is approximately normal.
In: Math
2. The IQ of humans is approximately normally distributed with a mean 100 and standard deviation of 15. A. What is the probablitlty that a randomly selected person has an IQ greater than 105? B. What is the probablitlty that a SPS of 60 randomly selected people will have a mean IQ greater than 105?
3. A 95% confidence interval for a population mean is (57,65). Can you reject the null hypothesis the mean= 68 at the 5% significance level why or why not?
In: Math
2. A researcher wishes to determine whether there is a
difference in the average age of elementary school, high school,
and community college teachers. Teachers are randomly selected from
each group. Their ages are recorded below. Test the claim that at
least one mean is different from the others. Use α = 0.01.
Resource: The OneWay ANOVA

Elementary School Teachers 
High School Teachers 
Community College Teachers 
23 
41 
39 
In: Math
A pollster surveyed a sample of 980 adult Americans, asking them if they own a personal firearm. 34% of the sample said yes.
1. What is a 90% confidence interval estimate for the percentage of Americans that own a firearm?
2. A gun owners’ group claims that more Americans own a firearm in 2015 than ten years ago, when the percentage of owners was 30%. At the 0.05 level of significance, has the percentage of owners increased?
3. What is the pvalue for this problem? How does it tell you what conclusion to draw about the null hypothesis?
In: Math
2 You are a researcher studying the affect of happiness between office workers, students, and musicians. Is there a difference in their affect of happiness?
Office workers 
Students 
Musicians 
23 
47 
88 
43 
77 
98 
56 
84 
78 
89 
55 
76 
45 
67 
82 
55 
76 
95 
23 
45 
79 
33 
67 
85 
27 
87 
94 
26 
66 
87 
In: Math
A research center survey of 2 comma 375 adults found that 1 comma 942 had bought something online. Of these online shoppers, 1 comma 274 are weekly online shoppers. Complete parts (a) through (c) below.
In: Math
The therm dataset contains information on survey respondents’ opinions about various public figures. These are “feeling thermometer” scores, which range from 0 (total dislike of the person) to 100 (total like). The relevant variables for this question are:
• white: a dummy variable indicating whether the respondent is white (ie, 1 for white and 0 for nonwhite)
• ideology: the respondent’s ideology on a scale of 1 (most liberal) to 7 (most conservative)
• obama: the respondent’s “feeling thermometer” score for Barack Obama
(a) One regression with obama as the dependent variable and white and ideology as the independent variables shows that
obama = 111.2 − 21.2 ∗ white − 8.7 ∗ ideology
What is the estimated intercept for white respondents? What about for nonwhite respondents?
(b) Another regression that includes a term for the interaction between white and ideology shows that
obama = 90.3+ 8.3∗white−3.0∗ideology−7.6∗(white ·ideology)
What are the estimated intercept and slope of ideology among white respondents? What about among nonwhite respondents? Is the relationship between ideology and Obama opinion stronger for white respondents, or nonwhite respondents?
In: Math
1. An ecologist is interested in studying the presence of different types of animal species in different locations. Using the following contingency table and the total sample size, rewrite the frequencies as relative frequencies. Round each relative frequency to two decimal places.
Location  bird species  mammal species  fish species 
A  21  4  6 
B  16  2  0 
C  3  1  7 
Location  bird species  mammal species  fish species 
A  
B  
C 
2. You are interested in learning about students' favorite mode of transportation at two universities. Fill in the blanks in the following contingency table, assuming that the variables are independent.
University  Bike  Car  Bus  Train  Other  Total 
A  592  300  204  80  1202  
B  410  335  20  55  1010  
Total  1002  635  394  44  135  2212 
3.Your teacher claims that the final grades in class are distributed as: A, 25%; B, 25%; C, 40%; D, 5%; F, 5%. At the end of a randomly selected academic quarter, the following number of grades are recorded. Calculate the appropriate chisquare test statistic that would be used to determine if the grade distribution for the course is different than expected. Round your answer to two decimal places.
Grade  A  B  C  D  F 
Number  36  42  58  10  14 
4. A dog breeder wishes to see if prospective dog owners have any preference among six different breeds of dog. A sample of 200 people (prospective dog owners) provided the data below. Find the critical chisquare value that would be used to test the claim that the distribution is uniform. Use α = 0.01 and round your answer to three decimal places.
Breed  1  2  3  4  5  6 
People  35  27  45  40  28  25 
In: Math
Calcium levels in people are normally distributed with a mean of 9.7mg/dL and a standard deviation of 0.3mg/dL. Individuals with calcium levels in the bottom 15
% of the population are considered to have low calcium levels. Find the calcium level that is the borderline between low calcium levels and those not considered low. Carry your intermediate computations to at least four decimal places. Round your answer to one decimal place.Calcium levels in people are normally distributed with a mean of
9.7mg/dL and a standard deviation of 0.3mg/dL. Individuals with calcium levels in the bottom 15% of the population are considered to have low calcium levels. Find the calcium level that is the borderline between low calcium levels and those not considered low. Carry your intermediate computations to at least four decimal places. Round your answer to one decimal place.
In: Math
A recent study found that children who watched a cartoon with food advertising ate, on average, 28.6 grams of crackers as compared to an average of 18.8 grams of crackers for children who watched a cartoon without food advertising. Suppose that there were 61 children in each group, and the sample standard deviation for those children who watched the food ad was 8.7 grams and the sample standard deviation for those children who did not watch the food ad was 7.7 grams. Complete parts (a) and (b) below.
b. Assuming that the population variances are equal, construct 95% confidence interval estimate of the difference μ1−μ2 between the mean amount of crackers eaten by the children who watch and do not watch the food ad.
___≤ μ1−μ2 ≤ ___ (Round to two decimal places as needed.)
In: Math
In: Math
Thirtyfour small communities in Connecticut (population near 10,000 each) gave an average of x = 138.5 reported cases of larceny per year. Assume that σ is known to be 41.7 cases per year.
(a) Find a 90% confidence interval for the population mean annual number of reported larceny cases in such communities. What is the margin of error? (Round your answers to one decimal place.)
lower limit  
upper limit  
margin of error 
(b) Find a 95% confidence interval for the population mean annual
number of reported larceny cases in such communities. What is the
margin of error? (Round your answers to one decimal place.)
lower limit  
upper limit  
margin of error 
(c) Find a 99% confidence interval for the population mean annual
number of reported larceny cases in such communities. What is the
margin of error? (Round your answers to one decimal place.)
lower limit  
upper limit  
margin of error 
(d) Compare the margins of error for parts (a) through (c). As the confidence levels increase, do the margins of error increase?
As the confidence level increases, the margin of error decreases.
As the confidence level increases, the margin of error remains the same.
As the confidence level increases, the margin of error increases.
(e) Compare the lengths of the confidence intervals for parts (a)
through (c). As the confidence levels increase, do the confidence
intervals increase in length?
As the confidence level increases, the confidence interval increases in length.
As the confidence level increases, the confidence interval remains the same length.
As the confidence level increases, the confidence interval decreases in length.
In: Math
An investment analyst has tracked a certain fund and found that it moves independently day to day, up or down a point. The probability of going up is 75%. What is the probability that four days from now, the price will be the same as now?
In: Math
A worldwide organization of academics claims that the mean IQ score of its members is 118, with a standard deviation of 16. A randomly selected group of 40 members of this organization is tested, and the results reveal that the mean IQ score in this sample is 115.8. If the organization's claim is correct, what is the probability of having a sample mean of 115.8 or less for a random sample of this size? Carry your intermediate computations to at least four decimal places. Round your answer to at least three decimal places.
In: Math