Show all work, partial credit will be given. Assume all assumptions have been met.

Show all work, partial credit will be given. Assume all assumptions have been met.

Name ________________________________________                              MTH 161               

Test 2                                                                                                                         50  points                                                                             

Show all work, partial credit will be given.  Assume all assumptions have been met.  This test is to be completed independently.  All problems are to be hand-calculated unless otherwise specified.

 

1. The Pew Research Center conducted a survey of 1007 adults and found that 856 of them know what Twitter is. (10 points)

 

1. What is the point estimate for the number of adults who know what Twitter is?

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1. Use a 0.01 level of significance to test the claim that more than 75% of adults know what Twitter is.

 

State the null and alternative hypotheses:

 

 

 

 

Calculate the test statistic:

 

 

 

 

 

 

 

 

Find the p-value:

 

 

 

Decision:

 

 

 

 

 

Conclusion:

 

 

 

 

 

 

2. Last year C&C Coffee Shop sold the following number of cups of coffee each month in their store.(8 Points)

Jan	Feb	Mar	Apr	May	Jun	Jul	Aug	Sept	Oct	Nov	Dec
152	148	100	165	155	138	120	145	161	125	140	158

Perform a hypothesis test, using α = 0.05, to determine if the 100 cups sold in March is an outlier.

 

 

 

 

 

 

 

 

 

 

 

 

 

3. The political parties of the winning candidates for a recent sequence of presidential elections are listed below. D denotes Democrat and R denotes Republican.  Does it appear, with 95% confidence, that we elect Democrat and Republican candidates randomly? (8 points)

 

R R D R D R R R R D D R R R D D D D D R R D D R R D R R R D D R R D

 

State the null and alternative hypotheses:

 

 

 

 

State the test statistic:

 

 

 

 

 

 

 

 

Determine the Critical Region:

 

 

 

 

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Decision:

 

 

 

Conclusion:

 

 

 

 

 

4. We make the claim that the proportion of females who are left handed is 18%. It is believed that it could actually be lower. We wish to reject H_o if the true proportion is 6% less than the hypothesized proportion. Use α = 0.01 and β = 0.02 to find the sample size necessary to test this claim.  (10 points)

 

State the null and alternative hypotheses:

 

 

 

 

Draw the curves and label α and β

 

 

 

 

 

 

 

 

Unstandardize and solve for “n”

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

5. The mean age of first time actresses who win an Oscar is believed to be 33 years old with a standard deviation of 11 years.With 95% confidence, we look at a random sample of 82 first time Oscar winners to test the theory that the mean age might be older than 33 years. (14 Points)

 

State the null and alternative hypotheses:

 

 

 

 

 

Calculate the value(s) of the sample mean that would cause us to reject H_o

 

 

 

 

 

 

 

 

 

 

Suppose the actual mean age is 35.9 years.  Calculate β

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