1. Dolly has seven books from the Statistics is Fun series. She plans on bringing three of the seven books with her in a road trip. How many different ways can the three books be selected? 2. Questions 2. involves the random variable x with probability
1. Dolly has seven books from the Statistics is Fun series. She plans on bringing three of the seven books with her in a road trip. How many different ways can the three books be selected?
2. Questions 2. involves the random variable x with probability distribution given below.
Show all work. Just the answer, without supporting work, will receive no credit.
|
x |
-1 |
0 |
1 |
2 |
|
P(x) |
0.1 |
0.3 |
0.4 |
0.2 |
– Determine the expected value of x.
– Determine the standard deviation of x. (Round the answer to two decimal places)
3. The heights of walnut trees are normally distributed with a mean of 9 feet and a standard deviation of 3 feet.
– What is the probability that a randomly selected walnut tree is greater than 12 feet?
– Find the 75th percentile of the walnut tree height distribution.
– If a random sample of 36 walnut trees is selected, what is the probability that the mean height of this sample is less than 10 feet?
4. A random sample of 100 light bulbs has a mean lifetime of 3000 hours. Assume that the population standard deviation of the lifetime is 500 hours. Construct a 95% confidence interval estimate of the mean lifetime. Show all work. Just the answer, without supporting work, will receive no credit.
5. Given a sample size of 100, with sample mean 730 and sample standard deviation 100, we perform the following hypothesis test at the 0.05 level.
H0:=750
H1: 750
– Determine the test statistic. Show all work; writing the correct test statistic, without supporting work, will receive no credit.
– Determine the critical values. Show all work; writing the correct critical value,
without supporting work, will receive no credit.
– What is your conclusion of the test? Please explain.
26. Consider the hypothesis test given by
H0:p=0.5
H1:p<0.5
In a random sample of 225 subjects, the sample proportion is found to be
P(hut)=0.51.
– Determine the test statistic. Show all work; writing the correct test statistic, without supporting work, will receive no credit.
–
– Determine the P-value for this test. Show all work; writing the correct P-value,
without supporting work, will receive no credit.
– Is there sufficient evidence to justify the rejection of
H0 at the =0.01 level? Explain.
7. In a study of memory recall, 5 people were given 10 minutes to memorize a list of 20 words. Each was asked to list as many of the words as he or she could remember both 1 hour and 24 hours later. The result is shown in the following table.
|
|
Number of words recalled |
|
|
subject |
1 hour later |
2 hour later |
|
1 |
14 |
12 |
|
2 |
18 |
15 |
|
3 |
11 |
9 |
|
4 |
13 |
12 |
|
5 |
12 |
12 |
Is there evidence to suggest that the mean number of words recalled after 1 hour exceeds the mean recall after 24 hours?
Assume we want to use a 0.01 significance level to test the claim.
(a) Identify the null hypothesis and the alternative hypothesis.
(b) Determine the test statistic. Show all work; writing the correct test statistic, without supporting work, will receive no credit.
(c) Determine the critical value. Show all work; writing the correct critical value,
without supporting work, will receive no credit.
(d) Is there sufficient evidence to support the claim that the mean number of words
recalled after 1 hour exceeds the mean recall after 24 hours? Justify your conclusion.
Refer to the following data for Questions 8 and 9.
|
x |
0 |
-1 |
3 |
5 |
|
y |
3 |
-2 |
3 |
8 |
8. Find an equation of the least squares regression line. Show all work; writing the correct equation, without supporting work, will receive no credit.
9. Based on the equation from # 8, what is the predicted value of y if x = 4? Show all work and justify your answer.
10. The store sells four different types of teddy bears. The manager reports that the four types are equally popular. Suppose that a sample of 100 purchases yields observed counts 30, 24, 22, and 24 for types 1, 2, 3, and 4, respectively.
|
type |
1 |
2 |
3 |
4 |
|
number |
30 |
24 |
22 |
24 |
Assume we want to use a 0.10 significance level to test the claim that the four types are equally popular.
(a) Identify the null hypothesis and the alternative hypothesis.
(b) Determine the test statistic. Show all work; writing the correct test statistic, without supporting work, will receive no credit.
(c) Determine the critical value. Show all work; writing the correct critical value,
without supporting work, will receive no credit.
(d) Is there sufficient evidence to support the manager’s claim that the four types are equally popular? Justify your answer.
