# Twenty Statistics Questions

Question 1

Which one of the following statements is true to perform a z-test for the difference between two population mean mu1 and mu2?

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: mu1 > mu2, alpha = 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. ¦ÒX1-X2 = ¦Ò(cap) ¡Ì(1/n1 + 1/n2) and d.f. = n1 + n2 - 2

b. ¦ÒX1-X2 = ¡Ì(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: ¦Ì1 ¡Ü ¦Ì2, ¦Á = 0.01, sample statistics:

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

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

Assume: ¦Ò1

2 ¡Ù ¦Ò2

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 ¦Á = 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: ¦Ìd = 0 (claim); Ha : ¦Ìd ¡Ù 0

b. Ho: ¦Ìd ¡Ý 0 ; Ha : ¦Ìd < 0 (claim)

c. Ho: ¦Ìd ¡Ü 0 (claim); Ha : ¦Ìd > 0

d. Ho: ¦Ìd ¡Ý 0 (claim); Ha : ¦Ìd < 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; ¦Á = 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 ¦Á = 0.1 and d.f.N = 4 and

d.f.D = 8 ?

a. 2.81

b. 2.69

c. 3.84

d. 3.69

See attached file for full problem description.

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#### Solution Preview

Question 1

Which one of the following statements is true to perform a z-test for the difference between two population mean ¦Ì1 and ¦Ì2?

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.

The z-test tests if there is a difference between the means of two samples or between the means of one sample and a population. For a two-sample z-test, the samples both have to be simple random samples, and either the samples have to come from a normal population or they have to be large

(at least 30). You also have to know the standard deviations of the populations the samples come from.

I think the answer is b, but I'm not 100% sure, because the question is worded poorly. I know that b is definitely correct. I think c is wrong, because the sample size doesn't have to be over 30 if the samples come from a normal population. If you don't know if the population is normal or not, then c would be true. I'm not sure if a is right or not ... in the paragraph above, I gave you three conditions that need to be met, but I've never heard any statistics teacher actually say "three conditions are required."

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.

Can you have more than one right answer for these questions? The definition of independent samples are samples selected from the same population, or different populations, that have no effect on one another (i.e. they are not correlated). Usually the samples are from different populations, because, for example, you are using the samples to test if the means of the populations are statistically significantly different.

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: ¦Ì1 > ¦Ì2, ¦Á = 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

Here, you want to use a two sample z-test (you use a z-test because you know the sample standard deviations). ...