Question

1. Which of the following is not as assumption for ANOVA:
   1. Equal sample sizes.
   2. All populations are normally distributed.
   3. Population variances are equal.
   4. All samples selected are random independent samples

2. If we want to test the level of general perception for groups of children 3 different villages, we use:
   1. ANOVA
   2. T-test
   3. Factor analysis
   4. Chi-square test

3. Analysis of variance is a statistical method of comparing the ________ of several populations.

a. standard deviations  

b. variances  

c. means  

d. proportions  

4. When the null hypothesis is rejected, we conclude that

a. the alternative hypothesis is false.

b. the alternative hypothesis is true.

c. the sample size is too large.

d. we used the wrong statistic.

5. When the p-value is smaller than the significance level

a. a Type I error is committed.

b. a Type II error is committed.

c. the null hypothesis is rejected.

d. the critical value is correct.

6. Restaurateur Denny Valentine is evaluating two sites, Raymondville and Rosenberg, for his next restaurant. He wants to prove that Raymondville residents (population 1) dine out more often than Rosenberg residents (population 2). Denny plans to test this hypothesis using a random sample of 81 families from each suburb. His alternate hypothesis is __________.

1. s₁² < s₂²
2. m₁- m₂ > 0
3. m₁- m₂< 0
4. m₁ - m₂ = 0

7. Lucy Baker is analyzing demographic characteristics of two television programs, COPS (population 1) and 60 Minutes (population 2). Previous studies indicate no difference in the ages of the two audiences. (The mean age of each audience is the same.) Lucy plans to test this hypothesis using a random sample of 100 from each audience. Her null hypothesis is ____________.

1. m₁ - m₂ ¹ 0
2. m₁ - m₂ > 0
3. m₁ - m₂ = 0
4. m₁ - m₂ < 0

1. Which of the following is not as assumption for ANOVA:
   1. Equal sample sizes.
   2. All populations are normally distributed.
   3. Population variances are equal.
   4. All samples selected are random independent samples

2. If we want to test the level of general perception for groups of children 3 different villages, we use:
   1. ANOVA
   2. T-test
   3. Factor analysis
   4. Chi-square test

3. Analysis of variance is a statistical method of comparing the ________ of several populations.

a. standard deviations  

b. variances  

c. means  

d. proportions  

4. When the null hypothesis is rejected, we conclude that

a. the alternative hypothesis is false.

b. the alternative hypothesis is true.

c. the sample size is too large.

d. we used the wrong statistic.

5. When the p-value is smaller than the significance level

a. a Type I error is committed.

b. a Type II error is committed.

c. the null hypothesis is rejected.

d. the critical value is correct.

6. Restaurateur Denny Valentine is evaluating two sites, Raymondville and Rosenberg, for his next restaurant. He wants to prove that Raymondville residents (population 1) dine out more often than Rosenberg residents (population 2). Denny plans to test this hypothesis using a random sample of 81 families from each suburb. His alternate hypothesis is __________.

1. s₁² < s₂²
2. m₁- m₂ > 0
3. m₁- m₂< 0
4. m₁ - m₂ = 0

7. Lucy Baker is analyzing demographic characteristics of two television programs, COPS (population 1) and 60 Minutes (population 2). Previous studies indicate no difference in the ages of the two audiences. (The mean age of each audience is the same.) Lucy plans to test this hypothesis using a random sample of 100 from each audience. Her null hypothesis is ____________.

1. m₁ - m₂ ¹ 0
2. m₁ - m₂ > 0
3. m₁ - m₂ = 0
4. m₁ - m₂ < 0

Answer 1

1. a. Equal sample sizes is not an assumption for ANOVA because we use F statistic here which can take two different sample sizes. or F(df1,df2) where df1 = n1 -1 and df2 = n2-1. Rest all are true.

2. a. ANOVA because we have to compare 3 villages (multiple comparisons). Here, we can compare on the whole if 3 villages are signifcant to level of perception.

3. b. Variances because we compare the variability explained by each component with unexplained variance/error to see if the populations are signifcantly different.

4. b. the alternative hypothesis is true because null hypothesis Ho is compared and tested for rejection against alternative hypothesis H1. Once we reject Ho, alternative hypothesis becomes true.

5. c. the null hypothesis is rejected because p-value is the probability of test statistic when Ho is true. When it is less than 0.05, it makes Ho an unexplainable or false event meaning thereby rejection of it.

6. b. m1- m2 > 0 because He wants to prove that Raymondville residents (population 1) dine out more often than Rosenberg residents (population 2).

7. c. m1 - m2 = 0 because Previous studies indicate no difference in the ages of the two audiences. (The mean age of each audience is the same.) Lucy plans to test this hypothesis using a random sample of 100 from each audience

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