# Florida University Standard Deviation Worksheet

QUESTION 1Among various ethnic groups, the standard deviation of heights is known to be approximately three inches. We wish to construct a

95% confidence interval for the mean height of male Swedes. Forty-eight male Swedes are surveyed. The sample mean is 71 inches.

The sample standard deviation is 2.8 inches. Fill in the blank with the appropriate value(s).

QUESTION 2

Among various ethnic groups, the standard deviation of heights is known to be approximately three inches. We wish to construct a

95% confidence interval for the mean height of male Swedes. Forty-eight male Swedes are surveyed. The sample mean is 71 inches.

The sample standard deviation is 2.8 inches.

b) We know the standard deviation for the population and the sample size is greater than 30, so we should use

the __________ distribution. (Choose one)

t

normal

(none)

chi square

QUESTION 3

Among various ethnic groups, the standard deviation of heights is known to be approximately three inches. We wish to construct a

95% confidence interval for the mean height of male Swedes. Forty-eight male Swedes are surveyed. The sample mean is 71 inches.

The sample standard deviation is 2.8 inches.

c) Construct a 95% confidence interval for the population mean height of male Swedes.

CI: (

,

)

QUESTION 4

Among various ethnic groups, the standard deviation of heights is known to be approximately three inches. We wish to construct a

95% confidence interval for the mean height of male Swedes. Forty-eight male Swedes are surveyed. The sample mean is 71 inches.

The sample standard deviation is 2.8 inches.

d) Choose the graph of the constructed 95% confidence interval for the population mean height of male Swedes.

QUESTION 5

The mean length of 84 randomly chosen upcoming engineering conferences (chosen from a list of every known upcoming engineering conference) was 3.94 days,

with a standard deviation of 1.28 days. Assume the underlying population is normal.

a) Choose the appropriate way to define random variables x and

x̄.

x is the length of an engineering conference.

x̄ is the mean length from a sample of 84 engineering conferences.

x is the mean length from a sample of 84 engineering conferences.

x̄ is the length of an engineering conference

x is 1.28 days

x̄ is the standard deviation

x is the number of conferences held in one day.

x̄ is the mean number of conferences held in one day.

QUESTION 6

A sample of 20 heads of lettuce was selected. Assume that the population distribution of head weight is normal. The weight of each head of lettuce was then

recorded. The mean weight was 2.2 pounds with a standard deviation of 0.1 pounds. The population standard deviation is known to be 0.2 pounds.

Identify the following:

a. x̄ =

b. σ =

c. n =

QUESTION 7

A sample of 20 heads of lettuce was selected. Assume that the population distribution of head weight is normal. The weight of each head of lettuce was then

recorded. The mean weight was 2.2 pounds with a standard deviation of 0.1 pounds. The population standard deviation is known to be 0.2 pounds.

Construct a 90% confidence interval for the population mean weight of the heads of lettuce.

(Write out to 4 decimal places and write as an interval. For example, (2,10) would be the interval from 2 to 10. )

CI: [a]

QUESTION 8

A sample of 20 heads of lettuce was selected. Assume that the population distribution of head weight is normal. The weight of each head of lettuce was then

recorded. The mean weight was 2.2 pounds with a standard deviation of 0.1 pounds. The population standard deviation is known to be 0.2 pounds.

Construct a 95% confidence interval for the population mean weight of the heads of lettuce.

(Write out to 4 decimal places and write as an interval. For example, (2,10) would be the interval from 2 to 10. )

CI: [a]

QUESTION 9

A toy factory makes 5,000 teddy bears per day. The supervisor randomly selects 10 teddy bears from all 5,000 teddy bears and uses this sample to estimate the

mean weight of teddy bears and the sample standard deviation. How many degrees of freedom are there in the estimate of the standard deviation?

QUESTION 10

Suppose that a committee is studying whether or not there is waste of time in our judicial system.

It is interested in the mean amount of time individuals waste at the courthouse waiting to be called for jury duty.

The committee randomly surveyed 81 people who recently served as jurors.

The sample mean wait time was eight hours with a sample standard deviation of four hours.

a) Find the following:

i) x̄ =

ii) sx=

iii) n=

iv) d.f.=

b) Which distribution should we use for this problem?

-distribution

c) Construct a 95% confidence interval for the population mean length of engineering conferences. CI: (

,

)

QUESTION 11

In a survey of 1400 social media users, 938 said they have made a purchase from an ad they found while using social media. Find:

a) The point estimate for the population proportion of social media users that have made a purchase from an ad they found while using social media.

p̂=

b) Construct a 95% confidence interval for the population proportion of social media users that have made a purchase from an ad they found while using social

media (3 decimal places).

margin of error, E:

confidence interval: (

,

)

QUESTION 12

A college professor wants to estimate the mean age of all of her students. In a random sample of 24 students, the mean age is found to be 21.5 years. The study

was done the previous year and produced a standard deiation of 1.2 years, where the population was normally distributed.

Find the standard error E and construct a 95% confidence interval of the population mean age

standard error, E:

CI: (

,

)

QUESTION 13

A poll of 35 employees from a particular store asked for their commute times to work . It showed a sample mean of 28.9 minutes with a sample standard deviation

of 7.0 minutes. Find the standard error E and construct a 99 percent confidence interval for the mean number of minutes it takes an employee to get to work.

E:

CI: (

,

)