HW #7 – Intro to Hypothesis Tests
Note that for each problem parts C through G are:
C) Give the critical value(s) (from the table).
D) Give the value of the test statistic (from the data).
E) Is the answer Yes or No?
F) What is the p-value?
G) Describe the meaning of the p-value in everyday terms.
Also all sample data are given at the end of the assignment.
1. (IN CLASS) Most people think that the average body temperature in adult humans is 98.6. However, this figure is based on data from the 1800’s. In a 1992 article in the Journal of the American Medical Association, it is reported a more accurate figure is 98.2. Assume a normal model is appropriate and that the population standard deviation is 0.7. We wish to see if we have good evidence at the 1% significance level that the mean of all adults is less than 98.6. Assume the data given at the end of the assignment.
A) Before collecting data, what is the probability of concluding the mean is less than 98.6 when it actually is not less than 98.6?
B) Before collecting data, what is the probability of not concluding the mean is less than 98.6 when it actually is less than 98.6?
2. (ANSWER GIVEN) Suppose the measurements on the stress needed to break a type of bolt follow a Normal distribution with a population standard deviation of 8.3 ksi. The advertised mean breaking strength is 80 ksi. We wish to see if we have good evidence at the 5% significance level that the mean breaking stress of all bolts is not 80 ksi.
A) Before collecting data, what is the probability of concluding the mean is not 80 ksi when it actually is 80 ksi?
B) Before collecting data, what is the probability of not concluding the mean is not 80 ksi when it actually is not 80 ksi?
3. (SOLUTION GIVEN) Assume the cholesterol levels of adult American women can be described by a Normal model with a population standard deviation of 24. We wish to see if we have good evidence at the 10% level of significance that the mean for the population of all adult American women is over 188.
A) Before collecting data, what is the probability of concluding the mean is over 188 when it actually is not?
B) Before collecting data, what is the probability of not concluding the mean is over 188 when it actually is?
4. (HOMEWORK) Biological measurements on the same species often follow a Normal distribution quite closely. Assume the weights of seeds of a variety of winged bean are approximately Normal with a population standard deviation of 110 mg. We wish to see if we have good evidence at the 5% significance level that the mean is over 525 for this variety.
A) Before collecting data, what is the probability of concluding the mean is over 525 when it actually is not?
B) Before collecting data, what is the probability of not concluding the mean is over 525 when it actually is?
5. (ALTERNATE HW) Assume the heights of women aged 20-29 follow approximately a Normal distribution with population standard deviation of 2.7 inches. We wish to see if we have good evidence at the 1% level of significance that the mean is not 64 inches.
A) Before collecting data, what is the probability of concluding the mean is not 64 inches when it actually is 64 inches?
B) Before collecting data, what is the probability of not concluding the mean is not 64 inches when it actually is not 64 inches?
6. (IN CLASS) We wish to see if we have good evidence at the 5% significance level that the mean time improvement for all possible participants in a fitness program to run a mile is more than 15 seconds after completing the program. Assume the time improvements are normally distributed with a population standard deviation of 70 seconds.
A) Before collecting data, what is the probability of concluding the mean is more than 15 seconds when it actually is not more than 15 seconds?
B) Before collecting data, what is the probability of not concluding the mean is more than 15 seconds when it actually is?
7. (ANSWER GIVEN) We wish to see if we have good evidence at the 1% significance level that the mean improvement in the number of sit-ups people could do in 5 minutes before and after an intense fitness class designed especially abs differs from 20. Assume the differences are normal with a population standard deviation of 40.
A) Before collecting data, what is the probability of concluding the mean is not 20 when it actually is 20?
B) Before collecting data, what is the probability of not concluding the mean differs from 20 when it actually does?
8. (SOLUTION GIVEN) We wish to see if there is any difference in the mean weights that two scales will report for the population of all cans of peaches that could ever be weighed. Assume the differences are normally distributed with a population standard deviation of 0.15. Use the 5% significance level.
A) Before collecting data, what is the probability of concluding a difference when there is no difference?
B) Before collecting data, what is the probability of not concluding a difference when there is a difference?
9. (HOMEWORK) We wish to see if we have good evidence at 10% level of significance if there is any difference in the population of all healthy adult females in the mean absorption into the blood between a generic drug and the reference name brand drug. We will at random give half the subjects the generic drug first and the rest will take the reference drug first. In all cases, a washout period separated the two drugs so that the first had disappeared before the subject took the second. Assume the population standard deviation is 1000.
A) Before collecting data, what is the probability of concluding a difference when there is no difference?
B) Before collecting data, what is the probability of not concluding a difference when there is a difference?
10. (ALTERNATE HW) We wish to see at the 5% significance level if there is any difference in the mean high temperatures in a big city at the airport and downtown. Assume the differences are normally distributed with a population standard deviation of 3.5 degrees.
A) Before collecting data, what is the probability of concluding a difference when there is no difference?
B) Before collecting data, what is the probability of not concluding a difference when there is a difference?
DATA:
1. SRS, sample size 30, sample mean 98.2.
2. SRS, sample size 32, sample mean 75.0.
3. SRS, sample size 50, sample mean 192.0.
4. SRS, sample size 48, sample mean 534.0.
5. SRS, sample size 42, sample mean 65.2.
6. SRS
Person / 1 / 2 / 3 / 4 / 5 / 6 / 7 / 8 / 9 / 10After / 580 / 611 / 542 / 570 / 542 / 540 / 490 / 490 / 488 / 490
Before / 630 / 660 / 560 / 542 / 580 / 585 / 500 / 522 / 533 / 544
Person / 11 / 12 / 13 / 14 / 15 / 16 / 17 / 18 / 19 / 20
After / 600 / 465 / 455 / 710 / 600 / 510 / 510 / 480 / 480 / 489
Before / 520 / 470 / 460 / 700 / 820 / 600 / 610 / 500 / 544 / 566
7. SRS
Person / 1 / 2 / 3 / 4 / 5 / 6 / 7 / 8 / 9 / 10 / 11After / 164 / 142 / 154 / 143 / 157 / 147 / 174 / 174 / 163 / 165 / 168
Before / 150 / 150 / 150 / 94 / 95 / 156 / 160 / 180 / 177 / 99 / 86
Person / 12 / 13 / 14 / 15 / 16 / 17 / 18 / 19 / 20 / 21
After / 192 / 182 / 195 / 176 / 193 / 184 / 152 / 142 / 190 / 183
Before / 162 / 162 / 133 / 165 / 165 / 165 / 166 / 166 / 172 / 172
Person / 22 / 23 / 24 / 25 / 26 / 27 / 28 / 29 / 30 / 31
After / 175 / 146 / 161 / 182 / 183 / 178 / 176 / 192 / 192 / 173
Before / 153 / 166 / 144 / 153 / 144 / 99 / 80 / 138 / 130 / 111
8. SRS
Can / 1 / 2 / 3 / 4 / 5 / 6 / 7 / 8 / 9 / 10 / 11Scale A / 11.83 / 12.46 / 11.87 / 12.99 / 12.33 / 13.30 / 12.73 / 11.55 / 13.31 / 12.26 / 12.13
Scale B / 11.71 / 12.44 / 11.91 / 12.58 / 11.88 / 13.49 / 13.11 / 11.02 / 12.99 / 11.58 / 12.07
Can / 12 / 13 / 14 / 15 / 16 / 17 / 18 / 19 / 20 / 21
Scale A / 12.41 / 12.51 / 12.14 / 12.17 / 12.80 / 12.27 / 11.57 / 12.57 / 11.59 / 11.64
Scale B / 12.78 / 12.38 / 11.68 / 11.95 / 12.81 / 12.38 / 11.36 / 11.48 / 11.50 / 11.45
9. SRS
Subject / A / B / C / D / E / F / G / H / I / JReference / 4110 / 2536 / 2769 / 3853 / 1832 / 2436 / 1999 / 1719 / 1829 / 2594
Generic / 1755 / 1148 / 1603 / 2254 / 1309 / 2120 / 1851 / 1878 / 1685 / 2643
Subject / K / L / M / N / O / P / Q / R / S / T
Reference / 2354 / 1864 / 1022 / 2256 / 938 / 1339 / 1262 / 1438 / 1735 / 920
Generic / 2738 / 2202 / 1254 / 3051 / 1287 / 1930 / 1964 / 2549 / 3335 / 3044
10. SRS
Day / 1 / 2 / 3 / 4 / 5 / 6 / 7 / 8 / 9 / 10 / 11 / 12 / 13 / 14 / 15 / 16 / 17Downtown / 72 / 74 / 61 / 90 / 88 / 46 / 52 / 60 / 70 / 44 / 32 / 60 / 60 / 45 / 93 / 97 / 80
Airport / 75 / 73 / 61 / 94 / 93 / 45 / 52 / 60 / 68 / 51 / 35 / 58 / 59 / 49 / 93 / 96 / 84