Reference no: EM132330116
Questions -
Q1. According to data from the American Medical Association, 10% of us are left-handed.
a. If 3 people are randomly selected, find the probability that they are all left-handed.
b. If 3 people are randomly selected, find the probability that at least one of them is left-handed.
c. If groups of 50 are randomly selected, what is the mean number of left-handed people in such groups?
d. If groups of 50 are randomly selected, what is the standard deviation for the numbers of left-handed people in such groups?
Q2. X has a normal distribution with a mean of 75.0 and a standard deviation of 2.5. Find the following probabilities:
a) P(x < 71.0)
b) P(72.5 < x < 79.0)
c) P(x > 82.5)
Q3. A sample of the math test scores of 35 fourth-graders has a mean of 82 with a standard deviation of 15.
Find the 95% confidence interval of the mean math test scores of all fourth-graders.
Find the 99% confidence interval of the mean math test scores of all fourth-graders.
Which interval is larger? Explain why.
Q4. A researcher is interested in estimating the average salary of fire fighters in a large city. He wants to be 95% confident that his estimate is correct. If the standard deviation is $1050, how large a sample is needed to get the desired information and to be accurate within $200?
Q5. A sample size of 35 is used to test H0: m 65 vs. Ha: < 65.
Given that = 63.5 and = 2.5, answer the following questions
a. What is the computed value of the test statistic?
b. What distribution does the test statistic have when the null hypothesis is true?
c. Is the alternative hypothesis one-tailed or two-tailed?
d. What is the p-value?
Q6. Mr. James McWhinney, president of Daniel-James Financial Services, believe there is a relationship between the number of client contacts and the dollar amount of sales. To document this assertion, Mr. Whinney gathered the following sample information. The X column indicates the number of client contacts last month, and the Y column shows the value of sales ($ thousands) last month for each client sampled.
|
# of Contacts X
|
Sales ($ thousands)
|
|
14
|
24
|
|
12
|
14
|
|
20
|
28
|
|
16
|
30
|
|
46
|
80
|
|
23
|
30
|
|
48
|
90
|
|
50
|
85
|
|
55
|
120
|
|
50
|
110
|
A. Determine the regression equation.
B. Determine the estimated sales 40 contacts are made.
Q7. A new model of digital camera is marketed in three major department store chains. The number of cameras sold every month at each of three store chains is listed below.
|
Target
|
K Mart
|
Wal Mart
|
|
187
|
164
|
180
|
|
200
|
144
|
213
|
|
191
|
170
|
198
|
|
188
|
151
|
214
|
At 0.05 level of significance, is there a difference in the mean numbers of cameras sold at the three department store chains?
A. State the null and the alternative hypothesis.
B. Compute SS total, SST, and SSE.
C. Develop an ANOVA table
D. What is the decision regarding the null hypothesis (is there a difference in the mean numbers of cameras sold at the three department store chains)?
Q8. The owner of a car dealership wants to determine whether there is a relation between the income level and the type of vehicle purchased in their dealership. He randomly sampled 500 car buyers and obtained the following data:
|
Income Level
|
SUV/Minivan
|
Midsize
|
Compact
|
|
up to $30K/yr
|
13
|
71
|
106
|
|
$30K-$60K
|
33
|
76
|
45
|
|
More than $60K/yr
|
66
|
59
|
31
|
At the .05 level of significance, determine whether there is a relation between the income level and the type of vehicle purchased. Show your work step by step.