# During an election, an exit poll is taken on 400 randomly selected

Practice Problems:  Chapter 8

1)  During an election, an exit poll is taken on 400 randomly selected voters and 214 of those polled voted for Candidate “Jim”.    A majority is needed to win the election.   We need to construct a Confidence Interval for the Population Proportion (p) of those who voted for Candidate “Jim” to determine whether we can declare Candidate “Jim” the likely winner on our nightly news broadcast.

A)     Construct a 90% Confidence Interval for the population proportion of voters who will vote for Candidate “Jim”.   This work is to be done by hand, not using software.

i)                    Test to see if we can use the normal approximation for the sample proportion.  Show all work

ii)                   If we can use the normal approximation, what is the Z multiplier

iii)                 What is the SE.   Show all work.

iv)                 Construct your interval, show your endpoints, and then indicate the width of the interval by subtracting the lower endpoint from the upper endpoint.  Show all work.

v)                  Can we declare Candidate “Jim” the likely winner?  Why?

B)      Construct a 95% Confidence Interval for the population proportion of voters who will vote for Candidate “Jim”.   This work is to be done by hand, not using software.

i)                    If we can use the normal approximation, what is the Z multiplier

ii)                   What is the SE.

iii)                 Construct your interval, show your endpoints, and then indicate the width of the interval by subtracting the lower endpoint from the upper endpoint.  Show all work

iv)                 Is the width the same, larger, or smaller than in Part A?   Why?

v)                  Can we declare Candidate “Jim” the likely winner?  Why?

C)      Construct a 95% Confidence Interval assuming 900 voters were polled and 482 indicated that they voted for Candidate “Jim”.

i)                    If we can use the normal approximation, what is the Z multiplier

ii)                   What is the SE.   Show all work.

iii)                 Construct your interval, show your endpoints, and then indicate the width of the interval by subtracting the lower endpoint from the upper endpoint.  Show all work

iv)                 Is the width the same, larger, or smaller than in Part B?   Why?

v)                  Can we declare Candidate “Jim” the likely winner?  Why?

2)  We want to estimate the population mean score (with 95% confidence) for a given achievement test.   We randomly sample 25 students.   The sample mean is 240 and the sample SD is 15.

A)     Construct a 95% Confidence Interval of the population mean score.

i)                    Calculate the SE of the sampling distribution of the sample mean

ii)                   What are the DF (degrees of freedom) and  t* multiplier from the

t-table in the back of the textbook?

Construct your 95% Confidence Interval for the population mean score, show your endpoints, and then indicate the width of the interval by subtracting the lower endpoint from the upper endpoint.  Show all work.

B)      Now assume our sample size is 81, with a sample mean of 240 and a sample SD of 15.    Construct a 95% Confidence Interval of the population mean score.

i)                    Calculate the SE of the sampling distribution of the sample mean

ii)                   What are the DF and t* multiplier from the t-table in the back of the textbook?

iii)                 Construct your 95% Confidence Interval, show your endpoints, and then indicate the width of the interval by subtracting the lower endpoint from the upper endpoint.   Show all work.

iv)                 Is the width the same, larger, or smaller than in part A?  Why?

v)                  Is 235 a possible value for the population mean score at this level of confidence?

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