MATH 1P98 - Assignment #4 | Complete Solution

MATH 1P98 - Assignment #4

Assignments must have a cover page (refer to the course outline).  Please write on one side of the page only and show ALL your work. Answer questions with sentences. Include any printout for a question with the question and clearly label the printout with the question number and part.

1) You have been assigned to test the hypothesis that the average number of cars waiting in line for the drive-thru window during lunch hour differs between Chick-fil-A, Wendy's, and McDonald's. The following data show the number of cars in line during randomly selected times during the lunch hour at all three chains.

Chick-fil-A
(1)    Wendy's
(2)    McDonald's
(3)
7    7    6
10    8    7
11    5    6
8    3    7
9    2    9

Perform a one-way ANOVA using α = 0.05 to determine if a difference exists in the average number of cars waiting in line at the drive-thru during the lunch hour between these chains.

MULTIPLE CHOICE.  Choose the one alternative that best completes the statement or answers the question.

Find the mean of the data summarized in the given frequency distribution.
2) The test scores of 40 students are summarized in the frequency distribution below. Find the mean score.

          2) _______

A) 66.6    B) 74.0    C) 70.3    D) 74.5

Find the indicated probability.
3) In a certain class of students, there are 11 boys from Wilmette, 4 girls from Winnetka, 7 girls from Wilmette, 4 boys from Glencoe, 5 boys from Winnetka and 4 girls from Glencoe.  If the teacher calls upon a student to answer a question, what is the probability that the student will be a boy?    3) _______

A) 0.429    B) 0.571    C) 0.71    D) 0.314

Find the indicated complement.
4) The probability that Luis will pass his statistics test is 0.49. Find the probability that he will fail his statistics test.    4) _______

A) 0.96    B) 0.51    C) 0.25    D) 2.04

Find the indicated probability.
5) 100 employees of a company are asked how they get to work and whether they work full time or part time.  The figure below shows the results. If one of the 100 employees is randomly selected, find the probability of getting someone who carpools or someone who works full time.
 
1. Public transportation: 10 full time, 7 part time
2. Bicycle:  3 full time, 3 part time
3. Drive alone:  30 full time, 35 part time
4. Carpool:  6 full time, 6 part time    5) _______

A) 0.55    B) 0.53    C) 0.61    D) 0.22

Find the indicated probability. Round to three decimal places.
6) In a study, 44% of adults questioned reported that their health was excellent. A researcher wishes to study the health of people living close to a nuclear power plant. Among 14 adults randomly selected from this area, only 3 reported that their health was excellent. Find the probability that when 14 adults are randomly selected, 3 or fewer are in excellent health.    6) _______

A) 0.020    B) 0.053    C) 0.046    D) 0.073

Solve the problem.
7) Human body temperatures are normally distributed with a mean of   and a standard deviation of   If 19 people are randomly selected, find the probability that their mean body temperature will be less than      7) _______

A) 0.4826    B) 0.0833    C) 0.3343    D) 0.9826

Use the given degree of confidence and sample data to construct a confidence interval for the population mean μ. Assume that the population has a normal distribution.
8) The amounts (in ounces) of juice in eight randomly selected juice bottles are:
     15.4  15.8  15.4  15.1
     15.8  15.9  15.8  15.7
Construct a 98% confidence interval for the mean amount of juice in all such bottles.    8) _______

A) 15.99 oz < μ < 15.23 oz    B) 15.33 oz < μ < 15.89 oz
C) 15.23 oz < μ < 15.99 oz    D) 15.89 oz < μ < 15.33 oz

Find the P-value for the indicated hypothesis test.
9) A random sample of 139 forty-year-old men contains 26% smokers. Find the P-value for a test of the claim that the percentage of forty-year-old men that smoke is 22%.    9) _______

A) 0.2542    B) 0.2802    C) 0.1271    D) 0.1401

State what the given confidence interval suggests about the two population means.
10) A researcher was interested in comparing the amount of time spent watching television by women and by men. Independent simple random samples of 14 women and 17 men were selected, and each person was asked how many hours he or she had watched television during the previous week. The summary statistics are as follows.
    
The following 99% confidence interval was obtained for   the difference between the mean amount of time spent watching television for women and the mean amount of time spent watching television for men:  -5.73 hrs < μ1 - μ2 < 4.13 hrs.
What does the confidence interval suggest about the population means?    10) ______

A) The confidence interval limits include 0 which suggests that the two population means are unlikely to be equal. There appears to be a significant difference between the mean amount of time spent watching television for women and the mean amount of time spent watching television for men.
B) The confidence interval includes only negative values which suggests that the mean amount of time spent watching television for women is smaller than the mean amount of time spent watching television for men.
C) The confidence interval limits include 0 which suggests that the two population means might be equal. There does not appear to be a significant difference between the mean amount of time spent watching television for women and the mean amount of time spent watching television for men.
D) The confidence interval includes only positive values which suggests that the mean amount of time spent watching television for women is larger than the mean amount of time spent watching television for men.

Determine which scatterplot shows the strongest linear correlation.
11) Which shows the strongest linear correlation?     11) ______
A)
     B)
     C)