# Homework Assignment - JustAnswer by liuhongmei

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1. If the test value in the figure below, for a test of the difference between two large sample means, is
2.57 when the critical value is 1.96, what decision about the hypothesis should be made?

A)   reject the null hypothesis
B)   accept the null hypothesis
C)   reject the alternative hypothesis
D)   not enough information

2. Determine the 95% confidence interval of the true difference in the means. A sociologist wants to
determine if the life expectancy of people in Africa is less than the life expectancy of people in Asia.
The data obtained is shown in the table below. Use   0.05 .
Africa        Asia
X        55.3          65.2
         8.1           9.3
n         53            42
A) 12.16   1   2  6.86
B) 13.46   1   2  6.34
C) 11.35   1   2  7.58
D) 16.33   1   2  5.98

3. A marketing firm asked a random set of married and single men as to how much they were willing to
spend for a vacation. At α = .05, is a difference in the two amounts?
Married men            Single men
Sample size                           60                   70
Mean spending                        260                  245
Sample variance                     5000                 6000
A) No, because the test value 0.09 is inside the interval (-1.96, 1.96)
B) No, because the test value 1.15 is inside the interval (-1.96, 1.96)
C) No, because the test value 1.20 is inside the interval (-1.96, 1.96)
D) No, because the test value 1.20 is outside the interval (-1.96, 1.96)

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4. An field researcher is gathering data on the trunk diameters of mature pine and spruce trees in a certain
area. The following are the results of his random sampling. Can he conclude, at α = .10, that the
average trunk diameter of a pine tree is greater than the average diameter of a spruce tree?
Pine trees            Spruce trees
Sample size                              80                    40
Mean trunk diameter (cm)                 40                    34
Sample variance                         110                   170
A) The data does not support the claim because the test value 1.07 is less than than 1.28.
B) The data supports the claim because the test value 2.53 is greater than than 1.28.
C) The data supports the claim because the test value 2.53 is greater than than 1.64.
D) The data does not support the claim because the test value 1.07 is less than than 1.64.

5. In comparing the two variances below, what is the test value and what are the degrees of freedom that
should be used?
Variance         Number of values
Sample 1                        5                    15
Sample 2                       10                    29
A) test value = 0.50, degrees of freedom = 15 and 29
B) test value = 0.50, degrees of freedom = 14 and 28
C) test value = 2.00, degrees of freedom = 14 and 28
D) test value = 2.00, degrees of freedom = 15 and 29

6. A car salesman claims that the variance of prices on convertibles is higher than the variance on station
wagons. The standard deviation of 16 convertibles is \$6800 and the standard deviation of 24 station
wagons is \$3900. For   0.05 , what is the test value?
A) 3.00
B) 3.04
C) 2.78
D) 2.33

7. A researcher hypothesizes that the variation in the car rental rates at a major cities' airport is less than
the car rental rates in that city. The variance of 7 airport car rental rates was \$30 and the variance of 6
city car rental rates was \$60. What is the test value?
A) 2.33
B) 1.41
C) 2.00
D) 4.00

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8. Determine the value of  as shown in the figure below, if the degrees of freedom were seven and nine.

A)   0.01
B)   0.025
C)   0.05
D)   0.1

9. In testing the equality of the two means below, what is the test statistic? (Use the unequal variances
formula)
Sample 1              Sample 2
Sample size                         9                    12
Sample mean                        80                    55
Sample variance                   450                    60
A) 2.31
B) 0.13
C) 0.45
D) 3.37

10. A medical researcher is interested in whether patients' left arms or right arms are longer. If 14 patients
participate in this study (so that n left arms and n left arms are measured), how many degrees of
freedom should the researcher use in her t-test critical value?
A) 13
B) 14
C) 26
D) 27

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11. A running coach wanted to see whether runners ran faster after eating spaghetti the night before. 24
random runners were chosen for this study. They ran a 5 kilometer race after having a normal dinner
the night before, and then a week later, reran the same race after having a spaghetti dinner the night
before. Their results (in seconds) are in the table below. At α = .01, what is the test value to use for
this test?
Regular Dinner        Spaghetti       Difference
Dinner         by runner
Sample mean                        1100               1080             –20
Sample variance                    2200               2800             350
A) –4.35
B) –1.07
C) –0.28
D) –5.24

12. One poll found that 47% of male voters will support a candidate while another found that 50% of
female voters will be in support. To test whether this candidate has equal levels of support between
male and female voters, the null hypothesis should be
A) H0 : pmale  pfemale
B) H0 : pmale 
50%, H0 : pfemale  50%
C) H0 : pmale 
47%, H0 : pfemale  50%
D) H0 : pmale  pfemale

13. One poll found that 34% of male voters will support a candidate while another found that 42% of
female voters will be in support. To test whether this candidate has equal levels of support between
male and female voters, the alternative hypothesis should be
A) H0 : pmale  pfemale
50%, H0 : pfemale  50%
B) H0 : pmale 
C) H0 : pmale 
34%, H0 : pfemale  42%
D) H0 : pmale  pfemale

14. A recent survey reported that in a sample of 300 students who attend two-year colleges, 105 work at
least 20 hours a week. In a sample of 225 students attending private universities, only 20 students
work at least 20 hours per week. What is the test value?
A) 6.95
B) 7.61
C) 2.38
D) 4.18

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15. When testing the difference between two proportions, one sample had 30 out of 100 who were for
capital punishment and the other sample had 60 out of 80 who were for capital punishment. Calculate
the standard error.
A) 0.075
B) 0.060
C) 0.042
D) 0.098

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