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# Testing of hypothesis and critical values

Question 1
Which one of the following statements is true to perform a z-test for the difference between two population mean &#956;1 and &#956;2?
a. Three conditions are required to perform such a test.
b. The samples must be independent and selected randomly.
c. Sample size must be at least 30.
d. All of the above.

Question 2
Two samples are independent if
a. Both of the samples are selected from same population.
b. One sample selected from a population is related to the sample selected from the same population.
c. One sample selected from a population is not related to the sample selected from the same population.
d. One sample selected from a population is not related to the sample selected from another population.

Question 3
Answer questions 3 and 4 from the following given data.
The data given below are taken from two independent samples collected randomly.
Claim: &#956;1 > &#956;2, &#945; = 0.10, sample statistics:
x1 (bar) = 500, s1 = 30, n1 = 100
x2 (bar) = 510, s2= 30, n2 = 75
What is the value of test statistics?
a. 0
b. -10
c. -25
d. 25

Question 4
What is the value of standardized test statistics?
a. 4.33
b. -4.33
c. 2.1822
d. -2.1822

Question 5
When sample sizes are less than 30 and the population variances are equal, we use t-test with standard error
a. &#963;X1-X2 = &#963;(cap) &#8730;(1/n1 + 1/n2) and d.f. = n1 + n2 - 2
b. &#963;X1-X2 = &#8730;(s1
2 /n1 + s2
2 /n2) and d.f. = smaller of n1 -1 or n2 - 1
C. Both A & B
d. Neither A nor B

Question 6
Answer questions 6 & 7 from the following given data:
Ho: &#956;1 &#8804; &#956;2, &#945; = 0.01, sample statistics:
x1 (bar) = 45, s1 = 4.8, n1 = 16
x2 (bar) = 50, s2= 1.2, n2 = 14
Assume: &#963;1
2 &#8800; &#963;2
2
What is the test statistics?
a. -5
b. 5
c. 2
d. -2
Question 7
What is the standardized test statistics?
a. -2.65
b. -4.025
c. 1.32
d. 3.067

Question 8
The requirement(s) to perform two-sample hypothesis test with dependent samples is/are:
a. Samples are selected randomly.
b. Samples are dependent.
c. Populations are normally distributed.
d. All of the above.

Question 9
Answer questions 9 - 13 for a = 0.10 using the following problem statement:
To test whether a fuel additive improves gas mileage, investigators measured the gas mileage (in miles per gallon) of nine cars with and without the fuel additive. At a level of &#945; = 0.10, can it be concluded that the additive improved gas mileage ? The results are shown below.
Identify the claim and Ho & Ha for this investigation.
Car 1 2 3 4 5 6 7 8 9
Gas mileage without additive 34.5 36.7 34.4 39.8 33.6 35.4 38.4 35.3 37.9
Gas mileage with fuel additive 36.4 38.8 36.1 40.1 34.7 38.3 40.2 37.2 38.7
a. Ho: &#956;d = 0 (claim); Ha : &#956;d &#8800; 0
b. Ho: &#956;d &#8805; 0 ; Ha : &#956;d < 0 (claim)
c. Ho: &#956;d &#8804; 0 (claim); Ha : &#956;d > 0
d. Ho: &#956;d &#8805; 0 (claim); Ha : &#956;d < 0

Question 10
Which one is the critical value to for this problem?
a. 1.611
b. 1.397
c. -1.611
d. -1.397

Question 11
What is the value of d(bar)?
a. 1.611
b. 1.397
c. -1.611
d. -1.397

Question 12
What is the value of sd?
a. 0.56
b. 0.66
c. 0.77
d. 0.89

Question 13
If we use t-test, what will be the standardized test statistic t?
a. -6.273
b. -3.653
c. -7.06
d. -3.0

Question 14 5
What will be the concluding decision for the following investigation?
Claim: p1 < p2; &#945; = 0.1
x1 = 471, n1 = 942; x2 = 372, n2 = 620
A. left-tailed test, reject Ho
B. right-tailed test, reject Ho
C. left-tailed test, fail to reject Ho
D. right-tailed test, fail to reject Ho

Question 15
Which of the following is true as a condition necessary to use the chi-square goodness of fit test?
a. The observed frequencies must be obtained using a random sample.
b. Each expected frequency must be at least 5.
c. None of the above.
d. Both of A & B.

Question 16
What is the expected frequency for n = 500, pi = 0.9?
a. 0.45
b. 4.50
c. 45.00
d. 450.00

Question 17
Answer questions 17 & 18 from the following table:
What is the expected frequency for 2nd row ? 2nd column, E2,2?
_ Ratings _
Size of restaurant Excellent Fair Poor Total
Seats 100 or fewer 182 203 165 550
Seats over 100 180 311 159 650
_ 362 514 324 1200
a. 165.92
b. 235.58
c. 196.08
d. 278.42

Question 18
What is the expected frequency for the 1st row - 3rd column, E1,3?
a. 148.50
b. 175.50
c. 278.42
d. 235.58

Question 19
Which statement is not true for an F-distribution?
a. The F-distribution is a family of curves.
b. The total area under each curve of an F-distribution is equal to 1.
c. F-distributions are normally distributed.
d. F-values are always at least 0.

Question 20
Which one is the critical F-value for a two-tailed test when &#945; = 0.1 and d.f.N = 4 and
d.f.D = 8 ?
a. 2.81
b. 2.69
c. 3.84
d. 3.69

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