__________________________________________________

These questions are similar to questions on the Problem Sets 3 and 4, and Discussion 15, but some numbers have changed.

Use the spaces provided. Submit your work as a single file document in pdf format.

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1. In a survey of 1010 people, 60% said that they voted in a recent presidential election. Voting records show that 61% of eligible voters actually did vote.

a. Find a 99% confidence interval estimate of the proportion of people who say that the voted. b. Are the survey results consistent with the actual voter turnout of 61 %? Why or Why not?

2. You plan to develop a new iOS social gaming app that you believe will surpass the success of Angry Birds and Facebook combined. In forecasting revenue, you need to estimate the percentage of all smartphone and tablet devices that use the iOS operating system versus Android and other operating systems. How many smartphones and tablets must be surveyed in order to be 99 % confident that your estimate is not in error by more than three percentage points?

a. Assume that nothing is known about the percentage of portable devices using the iOS operating system.

b. Assume that a recent survey suggests that about 47% of smartphone and tablets are using the iOS operating system.

c. Does the additional information from part (b) have much of an effect on the sample size that is required? Explain.

3. State the null and alternative hypotheses, find the P - Value, find the critical value, should we reject Ho, or should we fail to reject Ho at 5% level of significance (why or why not?) in the following situations:

a. The test statistic of Z = 1.50 is obtained when testing the claim that p > 0.3

b. The test statistic of Z = -2.00 is obtained when testing the claim that P < 0.75

c. The test statistic of Z = - 1.64 is obtained when testing the claim that p = 0.375

4. Use technology to find the P - Values. Would you reject or fail to reject Ho at 0.01 significance level? Why or why not? [Do 2ND (VARS) --- Select tcdf (lower value, upper value, degree of freedom), for lower value, use -99999 for lower tail of the T-distribution. Remember to multiple you answer by two for a two - tailed test]

a. The claim is that for Verizon data speeds at airports, the mean is 14.00 . mbps The size is n 14 and the test statistic is t 2.645.

b. The claim is that for 12 AM body temperatures, the mean is 98 . F

The size is n 8 and the

test statistic is t 2.603.

5. A study of seat belt use involved children who were hospitalized after motor vehicle crashes. For a group of 128 children who were wearing seat belts, the number of days in intensive care units (ICU) has a mean of 0.83 and a standard deviation of 1.77. For a group of 350 children who were not wearing seat belts, the number of days spent in ICUs has a mean of 1.39 and a standard deviation of 2.06 (based on data from some recorded research findings)

Use a 0.01 significance level to test the claim that children wearing seat belts have a lower mean length of time in an ICU than the mean for children not wearing seat belts. [Hint: STAT - TESTS -2-SampleTTest, and then complete the required statistics] Select the appropriate one below and complete the required values.

2 - SampTTest

Inpt: [Data] OR Inpt: [Stats]

List1: L1 x1:

List2: L2 Sx1:

Freq1: 1 n1:

Freq2: 2 x2 :

1: 2 2 2 Sx2 :

Pooled No Yes : n2 :

Calculate 1: 2 2 2

Pooled No Yes :

Calculate.

What is the test statistics? ______________________

What is the P - Value? __________________________ Should we reject or accept H0? __________________________ Give reasons for your answer____________________________ State your conclusion in the context of the problem.

6. Does prison really deter violent crimes? Let X represent percent change in the rate of violent crime and y represent percentage change in the rate of imprisonment in the general U. S. population. For seven recent years, the following data have been obtained.

X 6.3 6.0 3.6 4.2 6.2 6.5 8.1

Y

-1.0

-4.2

-6.2

-4.0

-3.6

-2.1

-4.4

a. Compute the value of the sample correlation coefficient r. (Round your value for r to be three decimal places)

b. Find the equation of the least-squares line y a bx (Round your value for a and b to be three decimal places)

c. Find the value of the coefficient of determination 2

r . What percentage of the variation

in y can be explained by the corresponding variation in x and the least - squares line? What percentage is unexplained? (Round your value for r to be three decimal places)

d. Considering the values of r and 2

r , does it make sense to use the least - squares line for

predictions. Explain your answers.

7. The blood types of 262 black homicide victims in Philadelphia have a distribution with 50% Type 0, 25% Type A, 20% Type B, and 5% Type AB.

Blood Type O A B AB Total

Frequency (O) 136 72 47 7 262

Expected Frequency(E)

E = np; n = 262

( ) O E

2

E

a. What is the expected frequency in each category? Complete the table.

2 ( ) O E

2

b. Compute

by completing the table above. Compute the P - value E

using: 2 2 [2 [ ] ( , 99, ) ] ND VARS cdf E df P value

c. At a significance level of 0.05, do you have statistically significant evidence that black homicide victims do not have the same distribution of blood types as the donor population? Give the reason for your answer. Remember to state the null and alternative hypotheses.

8. The table below lists the number of games played in the baseball World Series as of this Writing. The table also includes the expected 2 2 2

proportions of the number of games in a World Series, assuming that in each Series, both teams have about the same chance of winning. Use a 0.01 significance level to test the claim that the actual numbers of games fit the distribution indicated by the expected proportions.

Games Played 4 5 6 7 Total Actual World Series Contests (O) 20 28 50 30 Expected Proportions 3/16 4/16 5/16 4/16

Expected World Series

Contests(E)

E = np

[Hint:

1 2 O E E OR Store O in L and E in L use STAT TESTS GOF Test / , ]

Remember to state the null and alternative hypotheses. State your conclusion in the contest of the problem.

9. Responses to a survey question are broken down according to employment status and the sample results are given below. At the 0.05 significance level, test the claim that responses and employment status are independent.

YES NO UNDECIDED TOTAL

EMPLOYED 50 35 18

UNEMPLOYED 35 25 15

TOTAL

2 ( ) O E

2

Use these formulas given below. Test statistic

where O is the E

observed frequency in a cell and E is the expected frequency found by evaluating: OR USE TECHNOLOGY ( )( ) , ( 1)( 1)

row total column total E df r c

( )

grand total

2 [ ] 1: [ ] 2 3

ND x EDIT A x Enter the valuesinthe MATRIX

1

Then STAT TESTS Test Calculate and press ENTER

:

Note that the is P value

2

Remember to state the null and alternative hypotheses. State your conclusion in the context of the problem.

10. At the same time each day, a researcher records the temperature in each of three greenhouses. The table shows the temperatures in degrees Fahrenheit recorded for one week.

Greenhouse #1 Greenhouse #2 Greenhouse #3

73 71 69

72 69 67

73 72 62

66 72 71

68 65 65

71 73 68

72 71 72

69

65

62

Use a 0.01 significance level to test the claim that the average temperature is the same in each greenhouse. Remember to state the null and alternative

hypotheses.

To answer this question use 1 2 3 ANOVA L L L from TI ( , , ) 83 / 84 to an ANOVA table below [see page 578 for details Enter the data into your calculator: STAT1:Edit L1 for Greenhouse #1, L2 for Greenhouse #2, and L3 for Greenhouse #3 ].

Use P-value method for your test.

Source DF SS MS F P-Value Greenhouse

Error

Total