The data for a random sample of six paired observations are shown in the table. a. Calculatex and s b. Express , in terms of p, and ₂- c. Form a 90% confidence interval for Ha d. Test the null hypothesis Ho: H0 against the alternative hypothesis H, H*0. Use a=0.10. a. Calculate the difference between each pair of observations by subtracting observation 2 from observation 1. Find X- (Round to two decimal places as needed.) Calculate s (Round to two decimal places as needed.) b. If , and ₂ are the means of populations 1 and 2, respectively, express , in terms of μ, and ₂. Choose the correct answer below. OA. Hd H₂H₁ OB. Hd₁+H₂ OC. MH₁-H₂ OD. HH₂ + H₁ c. Form a 90% confidence interval for H (Round to two decimal places as needed.) d. Test the null hypothesis Ho: H0 against the alternative hypothesis H₂: H *0. Use a=0.10. Calculate the test statistic. (Round to two decimal places as needed.) Calculate the p-value. p-value= (Round to three decimal places as needed.) What is the appropriate conclusion of the hypothesis test at a = 0.10? OA. Do not reject Ho. There is sufficient evidence to indicate that μg 0. OB. Reject Ho. There is insufficient evidence to indicate that μg 0. OC. Reject Ho. There is sufficient evidence to indicate that µg 0 OD. Do not reject Ho. There is insufficient evidence to indicate that μg 0. Pair 1 2 3 4 5 6 Population 1 Sample (Observation 1) 6 3 6 4 7 Population 2 Sample (Observation 2) 6 6
The data for a random sample of six paired observations are shown in the table. a. Calculatex and s b. Express , in terms of p, and ₂- c. Form a 90% confidence interval for Ha d. Test the null hypothesis Ho: H0 against the alternative hypothesis H, H*0. Use a=0.10. a. Calculate the difference between each pair of observations by subtracting observation 2 from observation 1. Find X- (Round to two decimal places as needed.) Calculate s (Round to two decimal places as needed.) b. If , and ₂ are the means of populations 1 and 2, respectively, express , in terms of μ, and ₂. Choose the correct answer below. OA. Hd H₂H₁ OB. Hd₁+H₂ OC. MH₁-H₂ OD. HH₂ + H₁ c. Form a 90% confidence interval for H (Round to two decimal places as needed.) d. Test the null hypothesis Ho: H0 against the alternative hypothesis H₂: H *0. Use a=0.10. Calculate the test statistic. (Round to two decimal places as needed.) Calculate the p-value. p-value= (Round to three decimal places as needed.) What is the appropriate conclusion of the hypothesis test at a = 0.10? OA. Do not reject Ho. There is sufficient evidence to indicate that μg 0. OB. Reject Ho. There is insufficient evidence to indicate that μg 0. OC. Reject Ho. There is sufficient evidence to indicate that µg 0 OD. Do not reject Ho. There is insufficient evidence to indicate that μg 0. Pair 1 2 3 4 5 6 Population 1 Sample (Observation 1) 6 3 6 4 7 Population 2 Sample (Observation 2) 6 6
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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Transcribed Image Text:The data for a random sample of six paired observations are shown in the table.
a. Calculate X and s².
S
b. Express μ in terms of H₁ and
H₂.
c. Form a 90% confidence interval for μd.
d. Test the null hypothesis Ho: μ = 0 against the alternative hypothesis H₂: µå ‡0. Use α = 0.10.
a. Calculate the difference between each pair of observations by subtracting observation 2 from observation 1. Find Xd.
Xd=
(Round to two decimal places as needed.)
Calculate s
2
(Round to two decimal places as needed.)
b. If μ₁ and μ₂ are the means of populations 1 and 2, respectively, express μ in terms of μ₁ and µμ2. Choose the correct answer below.
A. Hd=H₂ H₁
B. Hd1₁H₂
OC. Hd H₁-H₂
O D. Hd=H₂ + H₂
c. Form a 90% confidence interval for μd.
(00)
(Round to two decimal places as needed.)
d. Test the null hypothesis Ho: μ = 0 against the alternative hypothesis H₂: Hd #0. Use α = 0.10. Calculate the test statistic.
t=
(Round to two decimal places as needed.)
Calculate the p-value.
p-value=
(Round to three decimal places as needed.)
What is the appropriate conclusion of the hypothesis test at α = 0.10?
O A. Do not reject Ho. There is sufficient evidence to indicate that μ‡0.
B. Reject Ho. There is insufficient evidence to indicate that μg 0.
O C. Reject Ho. There is sufficient evidence to indicate that μ‡0.
O D. Do not reject Ho. There is insufficient evidence to indicate that Hd
#0.
Pair
1
23456
Population 1 Sample
(Observation 1)
663647
Population 2 Sample
(Observation 2)
8
9
4
6
5
6
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Step 1: Given information:
VIEWStep 2: Calculate sample mean and sample variance for difference:
VIEWStep 3: Choose correction answer:
VIEWStep 4: Calculate 90% confidence interval for true mean difference:
VIEWStep 5: Set hypothesis and Calculate t-statistic:
VIEWStep 6: Calculate p-value:
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