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Stat: 2-2

#4: Determine the area under the standard normal curve that lies to the left of (a) Z = 1.72,

(b) Z = 0.66, (c) Z = 0.71, and (d) Z = 0.01.

(a) The area to the left of Z = 1.72 is _____.

(Round to four decimal places asneeded.)

(b) The area to the left of Z = 0.66 is _____.

(Round to four decimal places as needed.)

(c) The area to the left of Z = 0.71 is _____.

(Round to four decimal places as needed.)

(d) The area to the left of Z = 0.01 is _____.

(Round to four decimal places as needed.)

#5) Determine the area under the standard normal curve that lies between (a) Z = -1.55 and

Z = 1.55, (b) Z = – 2.75 and Z = 0, and (c) Z = -1.43 and Z = -0.92.

(a) The area that lies between Z = – 1.55 and Z = 1.55 is _____.

(Round to four decimal places as needed.)

(b) The area that lies between Z = – 2.75 and Z = 0 is _____.

(Round to four decimal places as needed.)

(c) The area that lies between Z = – 1.43Z and Z = – 0.92Z is _____.

(Round to four decimal places as needed.)

#6) Determine the total area under the standard normal curve in parts (a) through (c)

below.

(a) Find the area under the normal curve to the left of z = −2 plus the area under the

normal curve to the right of z = 22.

The combined area is 0.04550.0455.

(Round to four decimal places as needed.)

(b) Find the area under the normal curve to the left of z = − 1.52 plus the area under the

normal curve to the right of z = 2.52.

The combined area is _____.

(Round to four decimal places as needed.)

(c) Find the area under the normal curve to the left of z = – 0.25 plus the area under the

normal curve to the right of z = 1.40.

The combined area is _____.

(Round to four decimal places as needed.)

#9) The mean gas mileage for a hybrid car is 56 miles per gallon. Suppose that the gasoline

mileage is approximately normally distributed with a standard deviation of 3.2 miles per

gallon. (a) What proportion of hybrids gets over 60 miles per gallon? (b) What proportion

of hybrids gets 53 miles per gallon or less? (c) What proportion of hybrids get between 58

and 62 miles per gallon? (d) What is the probability that a random selected hybrid gets less

than 45 miles per gallon?

(a) The proportion of hybrids that gets over 60 miles per gallon is _____.

(Round to four decimal places as needed.)

(b) The proportion of hybrids that gets 53 miles per gallon or less is _____.

(Round to four decimal places as needed.)

(c) The proportion of hybrids that gets between 58 and 62 miles per gallon is

_____.

(Round to four decimal places as needed.)

(d) The probability that a randomly selected hybrid gets less than 45 miles per gallon is

_____.

(Round to four decimal places as needed.)

# 11) Suppose the lengths of the pregnancies of a certain animal are approximately

normally distributed with mean μ = 125 days and standard deviation σ = 12 days.

(a) What is the probability that a randomly selected pregnancy lasts less than 121 days?

The probability that a randomly selected pregnancy lasts less than 121 days is

approximately _____. (Round to four decimal places as needed.)

(b) What is the probability that a random sample of 13 pregnancies has a mean gestation

period of 121 days or less?

The probability that the mean of a random sample of 13 pregnancies is less than 121

days is approximately _____. (Round to four decimal places as needed.)

(c) What is the probability that a random sample of 37 pregnancies has a mean gestation

period of 121 days or less?

The probability that the mean of a random sample of 37 pregnancies is less than 121

days is approximately _____. (Round to four decimal places as needed.)

#13) Describe the sampling distribution of pˆ. Assume the size of the population is 25,000.

N = 900,

p = 0.1

(a) Determine the mean of the sampling distribution of pˆ. μˆp = _____

(Round to one decimal place as needed.)

(b) Determine the standard deviation of the sampling distribution of pˆ. σˆp = _____.

(Round to three decimal places as needed.)

#14) Suppose a simple random sample of size n=125 is obtained from a population whose

size is N = 30,000 and whose population proportion with a specified characteristic is p

equals 0.4.

(a) Determine the mean of the sampling distribution pˆ.

μˆp = _____ (Round to one decimal place as needed.)

Determine the standard deviation of the sampling distribution pˆ.

σˆp = _____. (Round to six decimal places as needed.)

(b) What is the probability of obtaining x = 55 or more individuals with the characteristic?

That is, what is P(pˆ ≥ 0.44)?

P(pˆ ≥ 0.44) = _____. (Round to four decimal places as needed.)

(c) What is the probability of obtaining x = 40 or fewer individuals with the characteristic?

That is, what is P(pˆ ≤ 0.32)?

P(pˆ ≤ 0.32) = _____ (Round to four decimal places as needed.)

2-3 Journal:

Using the Journal Dataset, consider the variable DP05 (days with precipitation that is more than

05 tenths of an inch). This is the number of days in each month that had 0.5 inches or more of

precipitation. For example, a value of 3 in DP05 means that during three days of that month, it

rained or snowed (equivalent) more than half an inch.

Draw a histogram of DP05. Does DP05 have an approximately normal distribution? Does it

have an obvious skew (left or right) and any obvious outliers? If an analysis requires that DP05

have a normal distribution, do you think that your results will be valid?

Now consider the variable EMXP (extreme maximum precipitation). That is the extreme

precipitation in each month, in tenths of a millimeter. For example, a value of 300 in EMXP

means that it rained 30 millimeters on the rainiest day of that month.

Draw a histogram of EMXP. Does EMXP have an approximately normal distribution? Does it

have an obvious skew (left or right) and any obvious outliers? If an analysis requires that EMXP

have a normal distribution, do you think that your results will be valid?

Stat 3-2

#3) Construct a confidence interval of the population proportion at the given level of

confidence. X = 860, n = 1100, 99% confidence

The upper bound of the confidence interval is _____.

(Round to the nearest thousandth as needed.)

The lower bound of the confidence interval is _____.

(Round to the nearest thousandth as needed.)

#5) In a trial of 300 patients who received 10-mg doses of a drug daily, 45 reported

headache as a side effect. Use this information to complete parts (a) through (d) below.

(a) Obtain a point estimate for the population proportion of patients who received 10-mg

doses of a drug daily and reported headache as a side effect.

pˆ = _____. (Round to two decimal places as needed.)

(b) Construct a 95% confidence interval for the population proportion of patients who

receive the drug and report headache as a side effect.

The 95% confidence interval is (_____, _____).

#6) A researcher wishes to estimate the proportion of adults who have high-speed Internet

access. What size sample should be obtained if she wishes the estimate to be within 0.01

with 90% confidence if

(a) she uses a previous estimate of 0.52?

(b) she does not use any prior estimates?

(a) n = _____ (Round up to the nearest integer.)

(b) n = _____ (Round up to the nearest integer.)

#9) Determine the point estimate of the population mean and margin of error for the

confidence interval.

Lower bound is 18, upper bound is 24.

The point estimate of the population mean is _____.

The margin of error for the confidence interval is _____.

#13) The following data represent the asking price of a simple random sample of homes for

sale. Construct a 99% confidence interval with and without the outlier included. Comment

on the effect the outlier has on the confidence interval.

$189,900

$143,000

$149,900

$170,500

$279,900

$205,800

$212,900

$147,800

$219,900

$154,500

$187,500

$264,900

(a) Construct a 99% confidence interval with the outlier included.

($_____, $_____) (Round to the nearest integer as needed.)

(b) Construct a 99% confidence interval with the outlier removed.

($_____, $_____) (Round to the nearest integer as needed.)

#14) A doctor wants to estimate the mean HDL cholesterol of all 20- to 29-year-old females.

How many subjects are needed to estimate the mean HDL cholesterol within 44 points with

99% confidence assuming s = 19.4 based on earlier studies? Suppose the doctor would be

content with 90% confidence. How does the decrease in confidence affect the sample size

required?

A 99% confidence level requires _____ subjects. (Round up to the nearest subject.)

A 90 % confidence level requires _____ subjects. (Round up to the nearest subject.)

Stat 4-2

#6) Determine the critical value for a left-tailed test regarding a population proportion at

the α = 0.01 level of significance.

Z = _____. (Round to two decimal places as needed.)

#7) Test the hypothesis using the classical approach and the P-value approach.

H 0 : p = 0.55 versus Upper H 1 : p <0.55
n = 150, x = 78, α = 0.10
b) Perform the test using the P-value approach.
P-value = _____ (Round to four decimal places as needed.)
#8) In a clinical trial, 22 out of 650 patients taking a prescription drug complained of
flulike symptoms. Suppose that it is known that 1.9% of patients taking competing drugs
complain of flulike symptoms. Is there sufficient evidence to conclude that more than 1.9%
of this drug's users experience flulike symptoms as a side effect at the α = 0.05 level of
significance?
What are the null and alternative hypotheses?
Upper H 0: p _ _____ versus Upper H1: p _ _____
Use technology to find the P-value.
P-value = _____ (Round to three decimal places as needed.)
#9) Several years ago, 46% of parents who had children in grades K-12 were satisfied with
the quality of education the students receive. A recent poll asked 1,195 parents who have
children in grades K-12 if they were satisfied with the quality of education the students
receive. Of the 1,951 surveyed, 467 indicated that they were satisfied. Construct a 99%
confidence interval to assess whether this represents evidence that parents' attitudes
toward the quality of education have changed.
What are the null and alternative hypotheses?
Upper H 0: p _ _____ versus Upper H 1: p _ _____
(Round to two decimal places as needed.)
Use technology to find the 99% confidence interval.
(_____, _____) (Round to two decimal places as needed.)
#10) In a survey, 34% 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 she
randomly selected 150 pet owners and discovered that 42 of them spoke to their pet on the
answering machine or telephone. Does the veterinarian have a right to be skeptical?
Use the α = _____ level of significance.
What are the null and alternative hypotheses?
Upper H 0: p_ _____ versus Upper H 1: p_ _____
(Round to two decimal places as needed.)
Use technology to find the P-value.
P-value = _____ (Round to three decimal places as needed.)
#11) Complete parts (a) through (c) below.
(a) Determine the critical value(s) for a right-tailed test of a population mean at the
α = 0.01 level of significance with 20 degrees of freedom.
(b) Determine the critical value(s) for a left-tailed test of a population mean at the
α = 0.10 level of significance based on a sample size of n = 15.
(b) Determine the critical value(s) for a two-tailed test of a population mean at the
α = 0.01 level of significance based on a sample size of n = 12.
(a) t Subscript critt =__ _____ (Round to three decimal places as needed.)
(b) t Subscript critt = __ _____ (Round to three decimal places as needed.)
(c) t Subscript critt equals= __ _____ (Round to three decimal places as needed.)
#12) To test Upper H 0: µ = 100 versus Upper H 1: µ ≠ 100, a simple random sample size of
n = 20 is obtained from a population that is known to be normally distributed.
Answer parts (a)-(d).
(a) If x over barx = 104.8 and s= 9.3, compute the test statistic.
t = ____ (Round to three decimal places as needed.)
(b) If the researcher decides to test this hypothesis at the α = 0.01 level of significance,
determine the critical values.
The critical values are _____, _____.
(Use a comma to separate answers as needed. Round to three decimal places as needed.)
#14) Several years ago, the reported mean age of an inmate on death row was 43.7 years. A
sociologist wondered whether the mean age of a death-row inmate has change since then.
She randomly selects 37 death-row inmates and finds that their mean age is 45.5, with a
standard deviation of 10.7. Construct a 99% confidence interval about the mean age of
death row inmates. What does the interval imply?
Choose the correct hypotheses.
Upper H 0: μ = __
Upper H 1: μ ≠ __
Construct a 99% confidence interval about the mean age.
(_____, _____) (Use ascending order. Round to two decimal places as needed.)
#15) It has long been stated that the mean temperature of humans is 98.6°F. However, two
researchers currently involved in the subject thought that the mean temperature of
humans is less than 98.6°F. They measured the temperatures of 148 healthy adults 1 to 4
times daily for 3 days, obtaining 500 measurements. The sample data resulted in a sample
mean of 98.3°F and a sample standard deviation of 0.90 °F.
Using the classical approach, judge whether the mean temperature of humans is less than
98.6°F at the α = 0.01 level of significance.
(a) Approximate the P-value
(b) The P-value is approximately _____. (Round to four decimal places as needed.)
4-3 Journal:
It is recommended that you begin the Module Four Discussion and Module Four Problem Set
before posting your journal entry.
For your fourth journal entry, consider again the variable DP05. Last week you constructed a
95% confidence interval for the number of months that had no days with 0.5 inches or more of
precipitation.
A resident thinks that 15% of the months have no days with 0.5 inches or more of precipitation.
Test this claim at a 0.05 significance level. How do your results compare to your 95% confidence
interval from the Module Three journal?
Now consider the variable EMNT. This is the extreme low temperature (extreme minimum
temperature) for the month, also reported in tenths of a degree Celsius. For example, a value of –
50 in EMNT means that the extreme low for the month was –5 degrees Celsius, or 23 degrees
Fahrenheit.
A resident thinks that the extreme low temperature during a randomly chosen month is about –5
degrees Celsius. Test this claim at a 0.01 significance level. Use both the classical method and
the p-value method. Does this analysis make sense?
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