week 7 quiz – A survey of American Society of Investors found

Subject: Mathematics    / Statistics
Question
Question 1

6.25 / 25 points

A survey of American Society of Investors found 30% of individual investors have used
a discount broker.
In a random sample of nine individuals, what is the probability that:

a.

Exactly two of the sample individuals have used a discount broker? P(x = 2)
Enter answer rounded to 3 or 4 decimal places with 0 to the left of the decimal
point.

b.

None of the 9 individuals have used a discount broker. P(X = 0)
Enter answer rounded to 3 or 4 decimal places with a 0 to the left of the decimal
point.

c.

Two or three individuals have used a discount broker. P( 2 <= X <= 3)
Enter answer rounded to 3 or 4 decimal places with a 0 to the left of the decimal
point.

d.

What is the mean and standard deviation for this distribution?
Enter each answer rounded to 2 decimal places in the order in which the
question was asked.

Question 2

0 / 25 points

A.C. Nielesen Company provides information to organizations advertising on television.
Prior research indicates that adult Americans watch an average of 6.0 hours of
television per day with a standard deviation of 1.5 hours.

Assuming the time distribution is normally distributed:
What is the probability that a randomly selected adult Americans watches 5 or more
hours of television per day?
Enter answer rounded to 3 or 4 decimal places with a 0 to the left of the decimal point.
Do not enter answer as a percent.

What is the probability that a randomly selected adult Americans watches between 7
and 8 hours (inclusive) of television per day?
Enter answer rounded to 3 or 4 decimal places with a 0 to the left of the decimal point.
Do not enter answer as a percent.

For how many hours per day must an adult American watch television in order to be in
the top 5% of all the adult American television watchers?
Enter answer rounded to 1 decimal place.

In a sample of 25 randomly selected adult Americans what is the probability that the
average time for watching television per day will be equal to or exceeds 6.5 hours?
Enter answer rounded to 3 decimal places with a 0 to the left of the decimal point. Do
not enter answer as a percent.

Question 3

18.75 / 25 points

The owner of the Britten’s Egg Farm wants to estimate the mean number of eggs
produced per chicken. A representative random sample of 20 chickens show they
produce an average of 25 eggs per month with a sample standard deviation (s) of 2

eggs per month. The distribution is known to be symmetrical and is close enough to
normal to be treated as a normal distribution.
Answer the following questions related to the above paragraph and then calculate a
90% confidence interval for the mean number of eggs produced per chicken on the
Britten’s Egg Farm.
What is the point estimate of the mean number of eggs produced per chicken?
Enter answer with 0 decimal places (integer).

What is the appropriate distribution for calculating a 90% confidence interval?
a

Uniform distribution

b

Normal distribution

c

t distribution

d

Chi Square distribution

Answer this question by entering the appropriate letter.

What is the degrees of freedom (dF) for the appropriate distribution. Enter Na if dF is
not required by the appropriate distribution.

Calculate the margin of error for the 90% confidence interval for the mean amount of
eggs laid per month on the Britten’s Egg Farm.
Enter answer rounded to 1 decimal point. Include a zero to the left of the decimal point
if the margin of error is a number between -1 and +1.

The 90% conference interval for the mean number eggs produced per month is:
Enter the lower and upper limits for the conference interval by entering the lower limit
first.
Rounded each conference limit to 1 decimal point.

Prior to this study the owner of the Britten’s Egg Farm Egg Farm believed the mean
amount off eggs produced per month on his farm was 30.
Does the study support his belief with a 90% confidence?
a Yes. The mean amount of eggs produced per month on his farm could be 30 per
month because the number 30 is not contained in the confidence interval.
b Yes. The mean amount of eggs produced per month on his farm could be 30 per
month because the number 30 is contained in the confidence interval.
c No. The mean amount of eggs produced per month on his farm is most likely not
30 per month because the number 30 is not contained in the confidence interval.
d No. The mean amount of eggs produced per month on his farm is most likely not
30 per month because the number 30 is contained in the confidence interval.
e The owner can not comment on the mean amount of eggs produced per month on
his farm because the confidence interval is based upon a sample.
Enter the correct answer by selecting and entering the appropriate letter.

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Question 4

5 / 25 points

The waiting time for customers at MacBerger Restaurants follows a normal distribution
with a population standard deviation of 1 minute.
At the Warren Road MacBerger, the quality assurance department sampled 49

customers and found that the mean waiting time was 2.75 minutes. At the .05
significance level, can we conclude that the mean waiting time is less than 3 minutes.
The Null Hypothesis is:
a

The waiting time for customers at MacBerger Restaurants is equal to

_______.

b

The waiting time for customers at MacBerger Restaurants is greater than _______.

c

The waiting time for customers at MacBerger Restaurants is less than

d

The waiting time for customers at MacBerger Restaurants is not equal to _______.

_______.

Enter the correct answer by selecting the appropriate letter and then entering the
correct number. Enter number to the same precision as presented in the question.

The Alternate Hypothesis is:
a

The waiting time for customers at MacBerger Restaurants is equal to

______.

b

The waiting time for customers at MacBerger Restaurants is greater than

______.

c

The waiting time for customers at MacBerger Restaurants is less than

______.

d

The waiting time for customers at MacBerger Restaurants is not equal to

______.

Enter the correct answer by selecting the appropriate letter and then entering the
correct number. Enter number to the same precision as presented in the question.

The appropriate distribution is:
a
b
c
d

Uniform Distribution
Normal Distribution
t Distribution
Chi Square Distribution

The Hypothesis test is a:
a
b
c

Left tail test
Right tail test
Two tail test

Enter the appropriate letters for answering the questions in the same order in which the
questions are asked.

Select and enter the letter for the appropriate decision rule.
Enter the critical value as a decimal rounded to 2 or 3 places.
Decision:
a
is

Ha hypothesis: If the test statistic is equal to or greater than the critical value which
_____.

b
is

Ha hypothesis: If the test statistic is equal to or less than the critical value which
_____.

c Ha hypothesis: If the absolute value of the test statistic is equal to or greater than
the critical value which is _____.

The numerical value of the test statistic is:
Enter answer rounded to 2 decimal places.

Hypothesis Test Decision:

a Null Hypothesis: Do not reject the null hypothesis. The data does not support the
Alternate Hypothesis.
b Alternate Hypothesis: Reject the null hypothesis. The data supports the Alternate
Hypothesis.
c The waiting time for customers at MacBerger Restaurants cannot be determined
because the data set is a sample.
Enter the correct answer by selecting the appropriate letter.

An alternate method for performing the Hypothesis Test would be to
calculate a Pvalue based upon the numerical value of the Test Statistic.
If the Pvalue is larger than the significance level of the test the appropriate
decision, based upon the numerical value of the test statistic, would be the
Null Hypothesis. If the Pvalue is less than or equal to the significance level of
the test the appropriate decision, based upon the numerical value of the test
statistic, would be the Alternate Hypothesis.
Based upon the data what is the Pvalue for the Hypothesis Test?
Enter answer as a decimal rounded to 2 places with a zero to the left of the
decimal point.
Do not enter answer as a percent.