1. A dietitian wants to compare the average calories in two kinds of loaves of bread, plain white and whole wheat. A simple random sample of 20 loaves of each type of bread from a local bakery results in the following:
| Plain White | Whole Wheat | |
| sample mean | 1800 | 1789 |
| sample standard deviation | 10 | 20 |
| sample size | 20 | 20 |
H0: ____________ Ha: _____________
Test Statistic:
d.f. = ______ ___________ < P-value < ___________
Conclusion in terms of this particular experiment:
2. What are p-values and how are they used in hypothesis testing?
(5 points)
3. If we say a statistical inference procedure is robust, what
does this mean? (5 points)
4. A recent newspaper article reported that 78% of people surveyed were opposed to televising trials. The article indicated that the study had a 3% margin of error. Assuming that this survey, like most such surveys reported, used a 95% confidence level, determine how many people were surveyed. Show your work. (6 points)
5. Most of our hypothesis tests and confidence interval
procedures require that randomization in sampling or experimentation has
occurred. Why? (5 points)
6. A manufacturer tests three different displays for selling a certain product by setting up a display in twelve different stores with similar overall sales so that each display type occurs in 4 stores. The number of units sold for one month is recorded for each of the 12 stores used. The manufacturer calculates the analysis of variance F test statistic and finds F = 4.63.
a. Give the degrees of freedom for this test and bracket the p-value for this test and interpret the result (in terms of this problem) using a 5% significance level. (6 points)Answer d.f. are ______ and ______ __________< p-value < __________
Conclusion:
b. What assumptions must hold for this test to be valid? (5 points)
7. Explain the difference between the terms standard error and standard
deviation. In answering this question, distinguish between these
two terms using a specific statistic, e.g., the sample mean.
(6 points)
8. Assuming that the population standard deviations
are equal, a test of
H0: µ1 = µ2 vs Ha: µ1
> µ2 with independent samples of sizes of n1
= 10 and n2 = 18 is completed and the calculated test statistic
is found to be t = 2.101. Give the degrees of freedom and bracket
the p-value for this test. (6 points)
Answer d.f. = ________ and
__________ < p-value < ___________
9. Researchers speculate that the proportion of left-handers
has grown with time because there is less tendency to force children into
right-handedness. A sample of 100 individuals of three different
age classes is taken to test this hypothesis. Use the results below
to answer the following questions:
|
|
|||
| Handedness | under 21 | 21 - 40 | 41 or above |
| Left | 20 | 10 | 3 |
| Right | 80 | 90 | 97 |
a. How many left-handers would we expect to observe in our sample of 100 individuals under twenty years of age, if the proportion of left-handers is the same for all age groups? (5 points)
Answer __________
b. A test of the hypothesis that the proportion of left-handedness is the same for all age groups is conducted and a test statistic of chi squared = 14.91 is found. Give the degrees of freedom and p-value for this test statistic and state your conclusion in terms of this problem using a 1% significance level. (6 points)10. Suppose you have just completed a hypothesis test and rejected the null hypothesis. Which of the following statements is correct? Write the letter of the correct statement in the space provided.Answer d.f. = ________ and _________< p-value < __________
Conclusion in terms of this problem:
c. Give a 95% confidence interval for the proportion of 21-40 year olds that are left handed. You need not carry out the calculations, simply put all the numbers in the correct places. (6 points)
a. You may have committed a type I error. Answer _________11. Define the power of a test and describe at least two methods to increase the power of a test.
b. You may have committed a type II error.
c. Both a and b are possible.
d. No error is possible.
12. Black spruce trees grow slowly in Alaska. Suppose they grow an average of 32 mm in height per year. An experiment is conducted using a sample of 17 black spruce trees under experimental conditions to determine if the rate of growth can be increased. The annual growth in millimeters for the experimental trees are as summarized in the stem plot below:
0| 1
1| 9
2| 467
3| 34799
4| 0123468
a. Give a 5 number summary for the growth of the 17 experimental trees and identify any outliers. (5 points)
13. A breeder of horses wants to determine the relationship between x = the gestation period and
b. Is it appropriate to use a one sample t procedure for testing H0: µ = 32 here? Why or why not? (Hint: discuss sample size, normality, etc.) (5 points)
| Horse | 1 | 2 | 3 | 4 | 5 | 6 | 7 |
| y = Life length in years | 24 | 25.5 | 20 | 21.5 | 22 | 23.5 | 21 |
| x = Gestation period in days | 416 | 279 | 298 | 307 | 356 | 403 | 265 |
a. Is there a significant linear relationship between length of life and gestation period? Justify your answer and use a significance level of 10%. (10 points)H0: ___________ versus Ha: ___________
Calculate the value of your test statistic: Show your work.
Give the d.f. = _______ __________ < p-value < _________
Conclusion in terms of this specific problem.
b. Give the mean and standard deviation of y = life length. (5 points)