Deck 9: Small Sample Inferences for Normal Populations

Question 1

Using the table for the t distributions, find the upper 0.005 point when d.f. = 1.

Answer 1

63.657

Question 2

Using the table for the t distributions, find the 99th percentile of the t distribution when d.f. = 2.

Answer 2

2.920

Question 3

Using the table for the t distributions, find the 97.5th percentile of the t distribution when d.f. = 11.

A) 2.201
B) 2.206
C) 2.211
D) 2.216

Answer 3

2.201

Question 4

Find the probability of T < -1.321 when d.f. = 22.

Question 5

Find the probability of | T | > 1.812 when d.f. = 10.

Question 6

Find the probability of -1.337 < T < 2.201 when d.f. = 16.

Question 7

Find the number b so that P[T < b] = .975 when d.f. = 6.

Question 8

The weights from a random sample of 21 Irish setter dogs have mean 61.7 pounds and standard deviation 5.8 pounds. Assume that the weights of the dogs have a normal distribution.

A) Construct a 95% confidence interval for the population.
B) What is the center of this confidence interval?

Question 9

According to health professionals, the incubation period for swine flu (the time between infection and appearance of symptoms) can be up to seven days, but it is most likely to be between two and five days. Recorded here are the incubation periods for seven infected persons.
5 4 2 4 5 6 5
Stating any assumption that you make, determine a 98% confidence interval for the true mean incubation period of this flu. Round your answer to two decimal places.

Question 10

One year at the university pool, the winning times(min) for the winner of the women's 200 meter free style were
What is the lower bound of a 98% confidence interval for the mean time?

A) 2.15
B) 2.22
C) 2.09
D) .52

Question 11

From a random sample of size 14, one has calculated the 98% confidence interval for $\mu$ and obtained the result (18.0, 24.2).
What was the $\bar{x}$ for the sample?

Question 12

From a random sample of size 18, one has calculated the 95% confidence interval for $\mu$ and obtained the result (18.6, 24.0).
What was the s for the sample?

Question 13

From a random sample of size 11, one has calculated the 95% confidence interval for $\mu$ and obtained the result (18.2, 28.4).
If the population standard deviation is unknown, calculate a 98% confidence interval for $\mu$ .

Question 14

For one country, the mean emissions of sulphur dioxide SO₂ (thousands of tons) was measured for 17 years. The yearly average was 7706 thousands of tons, with standard deviation 1582 thousands of tons. Compute a 95% confidence interval for the mean number of emissions of SO₂ .

Question 15

Consider the statistics about the lifetime of laptop L.C.D.s.
Is the population mean lifetime of all laptop L.C.D.s contained in this interval?

A) Yes
B) No
C) We do not know

Question 16

The coordinator of an advanced biology course took a random sample of the mid-term scores.
Do these data substantiate the conjecture that the population mean score is larger than 65 points? Test at $\alpha$ =0.01.

Question 17

Consider the total number of points scored in a football game. The sum of both teams scores from 20 football games randomly selected from one
National Football League season are:

Do these data substantiate a claim that the mean sum of points is greater than 40 points? Test with $\alpha$ =0.05.

Question 18

The following data shows the duration (in days) of eight randomly selected space shuttle missions.
Test the null hypothesis that the mean duration of a space shuttle mission is 13 days versus a two-sided alternative. Take $\alpha$ =0.05

Question 19

A random sample of size 12 from a normal population produced a 95% confidence interval (182.4, 191.2) based on the t distribution.
What is the conclusion of the t test for H₀: $\mu$ =179.1 versus H₁: $\mu$$\neq$ 179.1?

Question 20

The length (in seconds) of cellular phone calls in an industrial zone has a normal distribution. Suppose that, from a random sample of lengths, the t based 90% confidence interval for the population mean length is (83.4, 109.7) seconds. On the basis of the same sample, would H₀: $\mu$ =83.8 be rejected in favor of H₁: $\mu$$\neq$ 179.1 at $\alpha$ =0.01?
Answer the question "Yes", "No", or Cannot tell".

Question 21

The possible scores in a mathematics placement test are in the range 0 - 50. Recorded here are the scores obtained by eight students.

A) Construct a 95% confidence interval for the population mean scoreμ . Round your answer to one decimal place.

B) If you were to test H₀: μ=30 versus H₁: μ≠30 at α=0.05, what would you conclude from your result in part A. Answer "Rejected" or "not rejected".

Question 22

Using the table for the
distributions, find the upper 1% point when d.f. = 16. Round your answer to two decimal places.

Question 23

Find the probability of when d.f. = 12.

Question 24

Find the probability of when d.f. = 22.

A) .005
B) .005.
C) .1
D) .025

Question 25

Find the probability of when d.f. = 21.

Question 26

Refer to the following data set.

A) Obtain a 95% confidence interval for . Round your answer to three decimal places.
B) Obtain a 95% confidence interval for . Round your answer to two decimal places.

Question 27

Find a 98% confidence interval for on n = 25 and s = 0.425. Round your answer to two decimal places.

Question 28

The following data set shows the ages of 16 factory workers chosen at random.
Find a 90% confidence interval for based on these data. Round your answers to three decimal places.

Question 29

The following data set shows the ages of 16 factory workers chosen at random.
Based on these data, a 90% confidence interval for is (22.754, 12.262). The workers supervisor claims that . Do the data provide strong evidence that the workers population standard deviation is smaller than 18? Test with $\alpha$ =0.05.

Question 30

A naturalist measures the wing span of four butterflies. The data are
5 9 5 5
Let µ =population mean wingspan in centimeters.
(a) Formulate the hypotheses when the intent of the test is to show that µ > 4.2.
(b) Assuming that wing span has a normal distribution, conduct a test of hypotheses. Take α = .10
(c) Based on the conclusion to your test in Part a, what error could you have made.
(d) Explain why this possible error will seldom occur.

Question 31

A student documents a slow internet by observing the time , in minutes, that it takes to download five different web pages.
1 5 3 1 5
Let µ =population mean time in minutes.
(a) Formulate the hypotheses when the intent of the test is to show that µ /= 2.

(b) Assuming that the download time has a normal distribution, conduct a test of hypotheses. Take α = .10
(c) Based on the conclusion to your test in Part a, what error could you have made.

Question 32

To check on the five second rule, a student drops a slice of ripe wa- termelon on an inoculated piece of wood flooring. After 5 seconds, the amount of bacteria transferred is measured in percent transfer. This experiment is repeated nine more times. According to one formula for the percent transfer X, the summary statistics are
n = 10 $\bar{x}$ = 1.56 s = .08

Let µ =population mean transfer.
(a) Conduct a test of hypotheses with the intent of showing that
µ /= 1.5. Take $\alpha$ = .05.
(b) Explain your choice of sampling distribution and any assump- tion you made concerning the population distribution.
(c) Sketch the null distribution of your statistic and the rejection region.
(d) Based on the conclusion to your test in Part a, what error could you have made?

Question 33

The weights from a random sample of 16 adult golden doodle dogs have mean 66.4 pounds and standard deviation 4.8 pounds. As- sume that the weights of the dogs have a normal distribution.
Let µ =population mean number of times.
(a) Conduct a test of hypotheses with the intent of showing that
µ > 63 pounds. Take $\alpha$ = .05.
(b) Explain your choice of sampling distribution and any assump- tion you made concerning the population distribution.
(c) Sketch the null distribution of your statistic and the rejection region.
(d) Based on the conclusion to your test in Part a, what error could you have made?

Question 34

A student, wishing to document a slow internet, observes the time
, in minutes, that it takes to download a web page. The times for five pages are
1 5 3 1 5
Let µ =population mean time in minutes.
(a) Obtain a 97 % confidence interval for µ.
(b) Does your 97 % confidence interval cover µ. Explain.
(c) When a large number of these 97 % intervals are calculated, from data collected on different occasions, explain the reason you are 97% confident that any one of them covers µ.

Question 35

The weights from a random sample of 16 adult golden doodle dogs have mean 66.4 pounds and standard deviation 4.8 pounds. As- sume that the weights of the dogs have a normal distribution.
Let µ =population mean number of times.
(a) Obtain a 95 % confidence interval for the population mean µ.
(b) Does your interval cover µ? Explain.
(c) When a large number of these 95 % intervals are calculated, from data collected on different occasions, explain the reason you are 95% confident that any particular one of them covers µ.

Question 36

The weights from a random sample of 16 adult golden doodle dogs have mean 66.4 pounds and standard deviation 4.8 pounds. As- sume that the weights of the dogs have a normal distribution. Ob- tain a 95 % confidence interval for the population standard devia- tion ?