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1)
The null and alternative hypotheses are giving. Determine whether the hypothesis is left tailed;
right tailed; or two tailed. What parameter is being tested?
H0: p= 0.76
H1:p> 0.76
Chose the correct answer below
- Left tailed
-Right tailed
-Two tailed
What parameter is being tested?
a-σ
b-µ
c-p
2) Test the hypothesis using the classical approach and the P-value approach.
H0: p=0.45 versus H1: p<0.45
n=150, x=62, a=0.05
a) Perform the test using the classical approach; choose the correct answer below.
_Reject the null hypothesis
_There is not enough information to test the hypothesis
_Do not reject the null hypothesis
b) Perform the test using T-value approach.
P-value =………. (Round to four decimal places as needed)
Choose the correct answer below.
_ Reject the null hypothesis
_There is not enough information to test the hypothesis
_Do not reject the null hypothesis
3) In the poll 51% of the people polled answered yes to the question “Are you in the favor of death
venality for a person convicted of murder?” The margin of error in the poll was 2% and the
estimate was made with 94% confidence. At least how many people were surveyed?
The minimum number of surveyed people was ……… (Round up to the nearest integer)
4) A simple random sample of size n is drawn from a population that is normally distributed. The
sample mean, x, is found to be 107, and the sample standard deviation, s, is found to be 10.
a- Construct a 95% confidence interval about µ if the sample size, n, is 14
b- Construct a 95% confidence interval about µ if the sample size, n, is 26
c- Construct a 96% confidence interval about µ if the sample size, n, is 14
d-Could we have computed the confidence intervals in part (a)-(c) if the population had not
been normally distributed?
a- Construct a 95% confidence interval about µ if the sample size, n, is 14
(……..),(……..) (use ascending order. Round to one decimal place as needed)
b- Construct a 95% confidence interval about µ if the sample size, n, is 26
(…….),(……...) (use ascending order. Round to one decimal place as needed)
How does increasing he sample size affect the margin of error, E?
a-As the sample size increases the margin of error stays the same
b- As the sample size increases the margin of error decreases
c- As the sample size increases the margin of error increases
c- Construct a 96% confidence interval about µ if the sample size, n, is 14
(…..),(…..) (use ascending order. Round to one decimal place as needed)
Compare the results to those obtained in part (a) How does increase the level of confidence
affect the size f margin error?
a-As the percentage of confidence increases, the size of the interval stay the same
b- As the percentage of confidence increases, the size of the interval decreases
c- As the percentage of confidence increases, the size of the interval increases
d-Could we have computed the confidence intervals in part (a)-(c) if the population had not
been normally distributed?
a-Yes, the population does not need to be normally distributed
b-No, the population needs to be normally distributed
c-Yes, the population needs to be normally distributed
d-No, the population does not need to be normally distributed
5) State the conclusion based on the results of the test.
According to the report, the mean monthly cell phone bill was $48.52 three years ago. A researcher
suspects that the mean monthly cell phone bill is different today. The null hypothesis is rejected.
Choose the correct answer below
a- There is sufficient evidence to conclude that the mean monthly cell phone bill is different from
its level three years ago of $48.52.
b- There is sufficient evidence to conclude that the mean monthly cell phone bill is higher than its
level three years ago of $48.52.
c- There is not sufficient evidence to conclude that the mean monthly cell phone bill is different
from its level three years ago of $48.52.
6) Determine the point estimate of the population mean and margin of error for the confidence
interval.
Lower bound is 16, Upper bound is 28.
The point estimate of the population mean is ……….
The margin of error for the confidence interval is ………..
7) In a survey, 39% of the respondents stated that they talk to their pets on the answering machine
or telephone. A veterinarian believed this result to be too high, so he randomly selected 250
pets’ owners and discovered that 85 of them spoke to their pet on the answering machine or
telephone. Does he veterinarian have a right to be skeptical? Use the a = 0.1 level of
significance. Does the veterinarian have a right to be skeptical?
a- There is sufficient evidence to conclude that the true proportion of the pet owners who talk
to their pets on the answering machine or telephone is 39%
b- There is not sufficient evidence to conclude that the true proportion of the pet owners who
talk to their pets on the answering machine or telephone is 39%
c- There is not sufficient evidence to conclude that the true proportion of the pet owners who
talk to their pets on the answering machine or telephone is less than 39%
d- There is sufficient evidence to conclude that the true proportion of the pet owners who talk
to their pets on the answering machine or telephone is less than 39%
8) A real estate agent wants to estimate the average age of that baying investment property in his
area. He randomly selects 15 of his client who purchase investment properly and obtain the
data shown. Assume that σ = 10.2. Use this information to answer the following questions.
50 56 55 47 39
31 40 62 62 49
35 55 39 61 56
Use a data to compute a point estimate for the population mean age of real estate agent’s who
purchased investment property.
………..(Round to three decimal places as needed)
The buyer ages are approximately normally distributed and the sample does not contain any
outlier. Construct a 95% confidence interval for the mean age for all the real estate agent’s
clients who purchased investment properly.
(…….),(……) (used ascending order. Round to one decimal place as needed)
Interprets this interval
a- We are 95% confidence that the interval actually does contain the true value of the mean.
b- We are 95% confidence that the interval actually does not contain the true value of the
mean.
c- We are 95% chance that a true value of the mean will fall in the interval.
d- We are 95% chance that a true value of the mean will not fall in the interval.
9) It has long been stated that the mean temperature of human is 98.6 Degree F. However, two
researchers currently involved in the subject thought that the mean temperature of the sample
mean is less than 98.6 degree F. The measure the temperature of 148 healthy adults 1 to 4
times daily for 3 days, obtaining 700 measurements. The sample data resulted in a sample of
mean of 97.7 degree F. and the sample standard deviation of 0,6 degree F.
a-Using the classical approach, judge whether the mean temperature of human is less than 98.6
degree F. at the a = 0.01 level of significance.
b-Approximately the P-value.
(a) Choose the correct answer below.
a- Reject H0 since the test statistic is less than the critical value
b- Do not Reject H0 since the test statistic is not less than the critical value
c- Do not Reject H0 since the test statistic is less than the critical value
d- Reject H0 since the test statistic is not less than the critical value
(b) The P-value is approximately …….. (Round to four decimal place as needed)
10) A researcher is interested in approximately the mean number of miles on 4 year old cars of a
certain make and model. She finds a random of 12 such cars in her city and obtains the results
shoen.
45,335 29,005 51,003 44,414
47,974 57,144 30,440 46,171
30,110 54,003 38,797 41,437
Assume that the number of miles driven is normally distributed.
(a) Obtain the point estimate for the population mean number of miles on 4year old car of the
same make and model. X= ……… (Round to one decimal place as needed).
(b) Construct and interpret a 90% confidence interval for the population mean number of miles
on 4 years old car of same make and model. Assume σ =19,900.
A 90% confidence interval of the population mean number of miles on 4 year old car of the
same make and model is (……),(…….). (Use ascending order. Round to the nearest integer)
Choose the correct interpretation of the confidence interval.
a-The researcher is 90% confident that the mean number of miles is not in the interval.
b- The researcher is 90% confident that the mean number of miles is within the interval.
c-The probability that the interval contains the mean number of miles is 90%.
d- The probability that the interval does not contain the mean number of miles is 90%.
(c) Construct and interpret a 99% confidence interval for the population mean number of miles
on a 4 year old car of the same make and model is (…..),(……). (use ascending order. Round
to the nearest integer needed).
Choose the correct interpretation of the confidence interval.
a-The probability that the interval does not contain the mean number of miles is 99%.
b-The researcher is 99% confidence that the mean number of miles is not in the interval.
c- The researcher is 99% confidence that the mean number of miles is within the interval.
d- The probability that the interval contains the mean number of miles is 99%.
(d) What effect does increasing the level of confidence have on the interval?
- The width of the interval decreases.
- The width ot the interval increases.
(e) Do the confidence intervals computed in parts (b) and (c) represent an estimate for the
population mean number of miles on that specific make and model in the country? Why?
a-Yes because the simple size is larger enough, the results can be generalized to the entire
country.
b-Yes because the researcher simple all cars of the same age, make and model the results
can be generalized to the entire country.
c-No because the researcher only sampled cars in her own city, the results cannot be
generalized to the entire country.
d- No because the researcher simple all cars of the same age, make and model the results
can be generalized to the entire country.
11) To test H0: µ=100 versus H1:≠100, a random sample of size n=32 is obtained from a population
that is known to be normally distributed with σ=11.
(a) Does the population need to be normally distributed to compute the P-value?
(b) If the sample mean is determined to be x=97.2, compute the P-value.
(c) If the researcher decides to test this hypothesis at the a=0,02 level significance, will the
researcher reject the null hypothesis?
(a)Does the population need to be normally distributed to compute the P-value?
a-The population need to be normally distributed to compute the P-value since the sample
size is less than 30.
b-The population must be normally distributed to computed the P-value, regardless of the
sample size.
c- The population does not need to be normally distributed to compute the P-value since
the sample size is less than 30.
(b)Compute the P-value. Select the correct choice below and fill in any answer boxes in your
choice.
a- P-value= ……..(Round to four decimal place as needed).
b- The P-value cannot be computed.
(c)Will the researcher reject the null hypothesis?
a-No because the P-value is less than the level of significance.
b- No because the P-value is greater than the level of significance.
c- Yes because the P-value is greater than the level of significance.
d- Yes because the P-value is less than the level of significance.
e-It is undetermined; the P-value could not be computed.
12) (a) Determine the null and the alternative hypotheses, (b) explain what it would mean to make a
type I error, (c) explain what it would mean to make a type II error.
Three years ago, the mean price of a single family home was $243,771. A real estate broker
believes that the mean price has increased since then.
(a)Which of the following is the hypothesis test to be conducted?
A- H0: µ= $243,771; H1: µ> $243,771
B- H0: µ= $243,771; H1: µ ≠ $243,771
C- H0: µ= $243,771; H1: µ< $243,771
(b)Which of the following is a type I error?
a-The broker rejects hypothesis that the mean price is $243,771, when it is the true mean cost.
b- The broker rejects hypothesis that the mean price is $243,771, when the true mean price is
greater than $243,771.
c- The broker fails to reject hypothesis that the mean price is $243,771, when the true mean
price is greater than $243,771.
(c)Which of the following is the type II error?
a- The broker rejects hypothesis that the mean price is $243,771, when it is the true mean cost.
b- The broker fails to reject hypothesis that the mean price is $243,771, when the true mean
price is greater than $243,771.
c- The broker fails to reject hypothesis that the mean price is $243,771, when it is the true mean
cost.
(13) The mean consumption of the fruit three years ago was 97.7 pounds. A dietician believes that
the fruit consumption has risen since then.
(a)Determine the null and alternative hypotheses. Which of the following is correct?
A-H0: µ= 97.7; H1: µ ≠97.7
B- H0: µ= 97.7; H1: µ < 97.7
C- H0: µ= 97.7; H1: µ> 97.7
(b)Supposed the sample data indicate the null hypothesis should be rejected. State the
conclusion of the researcher. Which of the following is the conclusion that could be reached?
a-There is not sufficient evidence to conclude that the mean consumption of the fruit has risen.
b- There is not sufficient evidence to conclude that the mean consumption of the fruit has
stayed the same.
c-There is sufficient evidence to conclude that the mean consumption of the fruit has stayed the
same.
d-There is sufficient evidence to conclude that the mean consumption of the fruit has risen.
(c)Supposed, in fact, the mean consumption of the fruits is 97.7 pounds. Did the researcher
commit a type I or type II error?
a-The researcher committed a type II error because he accepted the alternative hypothesis
when the mean hypothesis was true.
b- The researcher committed a type II error because he rejected the null hypothesis when it was
true.
c- The researcher committed a type I error because he accepted the alternative hypothesis
when the mean hypothesis was true.
d- The researcher committed a type I error because he rejected the null hypothesis when it was
true.
If we tested this hypothesis at the a= 0.02 level of significance, what is the probability of
committing this error? (……….)
(14) A simple random sample of size n is drawn. The sample mean, x, is found to be 18.2, and the
sample standard deviation, s, is found to be 4.5.
(a)Construct a 95% confidence interval about µ if the sample size, n, is 34.
The confidence interval is (……), (…….). (Use ascending order. Round to two decimal places as needed)
(b) Construct a 95% confidence interval about µ if the sample size, n, is 51.
The confidence interval is (……), (…….). (Use ascending order. Round to two decimal places as needed)
How does increase the sample size affect the margin of error, E?
a-The margin of error does not change.
b-The margin of error increases.
c-The margin of error decreases.
(c)Construct a 99% confidence interval about µ if the sample size, n, is 34.
The confidence interval is (……), (…….). (Use ascending order. Round to two decimal places as needed)
Compare the result to those obtain in part (a). How does increasing the level of confidence affect the
size of margin of error, E?
a-The margin error increases.
b-The margin error does not change
c-The margin error decreases.
(d)If the sample size is 17, what conditions must be satisfied the confidence interval?
a-The sample data must come from a population that is normally distributed with outlier.
b- The sample must come from a population that is normally distributed and the sample size must be
large.
c- The sample size must be large and the sample should not have any outlier.
15) An agriculture researcher is interested in estimating the mean length of the growing season in a
region. Treating the last 10 years as a simple random sample, he obtains the following data, which
represent the number of days of the growing season.
151 159 145 147 163 193 187 175 164 155
(a) Because the sample size is small, we must verify that the data come from a population that is
normally distributed and that the sample size does not contain any outliers. The normal
probability plot and boxplot are shown bellow.
Are the conditions for constructing a confidence interval about the mean satisfied?
100
Percentage
80
250
Days
abcd-
130
230
Days
No the population is not normal
Yes, both condition are met
No, neither condition is met
No there are outliers
(b) Construct a 95% confidence interval for the mean length of the growing season in the region.
(……),(……). (Use ascending order. Round to two decimal places as needed.)
(c) What could be done to increase the accuracy of interval, assuming the researcher does not have
access to additional data?
a-The researcher could increase the sample mean.
b-The researcher could increase the level of confidence.
c- The researcher could decrease the level of confidence.
d- The researcher could decrease the sample standard deviation.