# 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 μ1 and μ2?

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: μ1 > μ2, α = 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. σX1-X2 = σ(cap) √(1/n1 + 1/n2) and d.f. = n1 + n2 - 2

b. σX1-X2 = √(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: μ1 ≤ μ2, α = 0.01, sample statistics:

x1 (bar) = 45, s1 = 4.8, n1 = 16

x2 (bar) = 50, s2= 1.2, n2 = 14

Assume: σ1

2 ≠ σ2

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 α = 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: μd = 0 (claim); Ha : μd ≠ 0

b. Ho: μd ≥ 0 ; Ha : μd < 0 (claim)

c. Ho: μd ≤ 0 (claim); Ha : μd > 0

d. Ho: μd ≥ 0 (claim); Ha : μd < 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; α = 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 α = 0.1 and d.f.N = 4 and

d.f.D = 8 ?

a. 2.81

b. 2.69

c. 3.84

d. 3.69