Question

(Round all intermediate calculations to at least 4 decimal places.) Consider the following competing hypotheses and...

(Round all intermediate calculations to at least 4 decimal places.)

Consider the following competing hypotheses and relevant summary statistics:

H0: σ21/σ22σ12/σ22 = 1
HA: σ21/σ22σ12/σ22 ≠ 1
Sample 1: x¯x¯1 = 46.5, s21s12 = 19.1, and n1 = 7
Sample 2: x¯x¯2 = 49.9, s22s22 = 17.2, and n2 = 5
Assume that the two populations are normally distributed. Use Table 4.

a-1.

Calculate the value of the test statistic. Remember to put the larger value for sample variance in the numerator. (Round your answer to 2 decimal places.)

  Test statistic   

a-2.

Approximate the p-value.
0.05 < p-value < 0.10
p-value > 0.20
0.02 < p-value < 0.05
0.10 < p-value < 0.20

a-3.

Do you reject the null hypothesis at the 10% significance level?
No, since the p-value is more than α.
No, since the p-value is less than α.
Yes, since the p-value is less than α.
Yes, since the p-value is more than α.

  

b-1.

Calculate the critical value at the 10% significance level. (Round your answer to 2 decimal places.)

  

  Critical value   

b-2.

Do you reject the null hypothesis at the 10% level?
  
Yes, since the value of the test statistic is less than the critical value.
No, since the value of the test statistic is more than the critical value.
Yes, since the value of the test statistic is more than the critical value.

No, since the value of the test statistic is less than the critical value.

Homework Answers

Answer #1

a-1.

Test statistic, F = S12 / S22 = 19.1 / 17.2 = 1.11

a-2.

Numerator degree of freedom = n1 - 1 = 7 - 1 = 6

Denominator degree of freedom = n2 - 1 = 5 - 1 = 4

P-value = P(F > 1.11) = 0.4816

Thus, p-value > 0.20

a-3.

Since, the p-value is more than α., we fail to reject the null hypothesis.

No, since the p-value is more than α.

a-4.

Critical value at the 10% significance level at df = 6, 4

F = 6.16

a-4.

Since the value of the test statistic is less than the critical value, we fail to reject the null hypothesis.

No, since the value of the test statistic is less than the critical value.

Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
(Round all intermediate calculations to at least 4 decimal places.) Consider the following hypotheses: H0: μ...
(Round all intermediate calculations to at least 4 decimal places.) Consider the following hypotheses: H0: μ =208 HA: μ < 208 A sample of 74 observations results in a sample mean of 202. The population standard deviation is known to be 26. Use Table 1 a. What is the critical value for the test with α = 0.10 and with α = 0.01? (Negative values should be indicated by a minus sign. Round your answers to 2 decimal places.) Critical...
(Round all intermediate calculations to at least 4 decimal places.) Consider the following hypotheses: H0: μ...
(Round all intermediate calculations to at least 4 decimal places.) Consider the following hypotheses: H0: μ ≥ 177 HA: μ < 177 A sample of 84 observations results in a sample mean of 170. The population standard deviation is known to be 24. Use Table 1. a. What is the critical value for the test with α = 0.05 and with α = 0.01? (Negative values should be indicated by a minus sign. Round your answers to 2 decimal places.)...
(Round all intermediate calculations to at least 4 decimal places.) A recent study by Allstate Insurance...
(Round all intermediate calculations to at least 4 decimal places.) A recent study by Allstate Insurance Co. finds that 82% of teenagers have used cell phones while driving (The Wall Street Journal, May 5, 2010). In October 2010, Massachusetts enacted a law that forbids cell phone use by drivers under the age of 18. A policy analyst would like to determine whether the law has decreased the proportion of drivers under the age of 18 who use a cell phone....
Consider the following competing hypotheses and accompanying sample data. Use Table 1. H0 : P1− P2...
Consider the following competing hypotheses and accompanying sample data. Use Table 1. H0 : P1− P2 = 0.20 HA : P1− P2 ≠ 0.20   x1 = 150 x2 = 130   n1 = 250 n2 = 400 a. Calculate the value of the test statistic. (Round intermediate calculations to at least 4 decimal places and final answer to 2 decimal places.)   Test statistic    b. Approximate the p-value. p-value < 0.01 0.01 ≤ p-value < 0.025 0.025 ≤ p-value < 0.05...
Consider the following competing hypotheses and accompanying sample data drawn independently from normally distributed populations. (Note:...
Consider the following competing hypotheses and accompanying sample data drawn independently from normally distributed populations. (Note: the automated question following this one will ask you confidence interval questions for this same data, so jot down your work.) H0: μ1 − μ2 = 0 HA: μ1 − μ2 ≠ 0    x−1x−1 = 74 x−2x−2 = 65   σ1 = 1.57 σ2 = 14.10   n1 = 19 n2 = 19 a-1. Calculate the value of the test statistic. (Negative values should be indicated...
(Round all intermediate calculations to at least 4 decimal places.) An entrepreneur owns some land that...
(Round all intermediate calculations to at least 4 decimal places.) An entrepreneur owns some land that he wishes to develop. He identifies two development options: build condominiums or build apartment buildings. Accordingly, he reviews public records and derives the following summary measures concerning annual profitability based on a random sample of 32 for each such local business ventures. For the analysis, he uses a historical (population) standard deviation of $21,900 for condominiums and $19,900 for apartment buildings. (You may find...
Consider the following competing hypotheses and accompanying sample data drawn independently from normally distributed populations. (You...
Consider the following competing hypotheses and accompanying sample data drawn independently from normally distributed populations. (You may find it useful to reference the appropriate table: z table or t table) H0: μ1 − μ2 = 0 HA: μ1 − μ2 ≠ 0 x−1x−1 = 75 x−2x−2 = 79 σ1 = 11.10 σ2 = 1.67 n1 = 20 n2 = 20 a-1. Calculate the value of the test statistic. (Negative values should be indicated by a minus sign. Round all intermediate...
Consider the following competing hypotheses and accompanying sample data drawn independently from normally distributed populations. (You...
Consider the following competing hypotheses and accompanying sample data drawn independently from normally distributed populations. (You may find it useful to reference the appropriate table: z table or t table) H0: μ1 − μ2 = 0 HA: μ1 − μ2 ≠ 0 x−1x−1 = 57 x−2x−2 = 63 σ1 = 11.5 σ2 = 15.2 n1 = 20 n2 = 20 a-1. Calculate the value of the test statistic. (Negative values should be indicated by a minus sign. Round all intermediate...
Consider the following competing hypotheses and accompanying sample data drawn independently from normally distributed populations. (You...
Consider the following competing hypotheses and accompanying sample data drawn independently from normally distributed populations. (You may find it useful to reference the appropriate table: z table or t table) H0: μ1 − μ2 = 0 HA: μ1 − μ2 ≠ 0 x−1x−1 = 68 x−2x−2 = 80 σ1 = 12.30 σ2 = 1.68 n1 = 15 n2 = 15 a-1. Calculate the value of the test statistic. (Negative values should be indicated by a minus sign. Round all intermediate...
(Round all intermediate calculations to at least 4 decimal places.) An entrepreneur owns some land that...
(Round all intermediate calculations to at least 4 decimal places.) An entrepreneur owns some land that he wishes to develop. He identifies two development options: build condominiums or build apartment buildings. Accordingly, he reviews public records and derives the following summary measures concerning annual profitability based on a random sample of 32 for each such local business ventures. For the analysis, he uses a historical (population) standard deviation of $22,900 for condominiums and $19,700 for apartment buildings. (You may find...