Education influences attitude and lifestyle. Differences in education are a big factor in the "generation gap." Is the younger generation really better educated? Large surveys of people age 65 and older were taken in n₁ = 34 U.S. cities. The sample mean for these cities showed that x₁ = 15.2% of the older adults had attended college. Large surveys of young adults (age 25 - 34) were taken in n₂ = 31 U.S. cities. The sample mean for these cities showed that x₂ = 19.1% of the young adults had attended college. From previous studies, it is known that ₁ = 6.2% and ₂ = 4.4%. Does this information indicate that the population mean percentage of young adults who attended college is higher? Use a = 0.05. (a) What is the level of significance? State the null and alternate hypotheses. o Hỏi H = Hi Hi Hi * tha o Hoi thi = Khai Hai Hit о н н H₂ (b) What sampling distribution will you use? What assumptions are you making? O The Student's t. We assume that both population distributions are approximately normal with unknown standard deviations. O The standard normal. We assume that both population distributions are approximately normal with known standard deviations. O The Student's t. We assume that both population distributions are approximately normal with known standard deviations. O The standard normal. We assume that both population distributions are approximately normal with unknown standard deviations. What is the value of the sample test statistic? (Test the difference #₁ #₂. Round your answer to two decimal places.) *** (c) Find (or estimate) the P-value. (Round your answer to four decimal places.)
Education influences attitude and lifestyle. Differences in education are a big factor in the "generation gap." Is the younger generation really better educated? Large surveys of people age 65 and older were taken in n₁ = 34 U.S. cities. The sample mean for these cities showed that x₁ = 15.2% of the older adults had attended college. Large surveys of young adults (age 25 - 34) were taken in n₂ = 31 U.S. cities. The sample mean for these cities showed that x₂ = 19.1% of the young adults had attended college. From previous studies, it is known that ₁ = 6.2% and ₂ = 4.4%. Does this information indicate that the population mean percentage of young adults who attended college is higher? Use a = 0.05. (a) What is the level of significance? State the null and alternate hypotheses. o Hỏi H = Hi Hi Hi * tha o Hoi thi = Khai Hai Hit о н н H₂ (b) What sampling distribution will you use? What assumptions are you making? O The Student's t. We assume that both population distributions are approximately normal with unknown standard deviations. O The standard normal. We assume that both population distributions are approximately normal with known standard deviations. O The Student's t. We assume that both population distributions are approximately normal with known standard deviations. O The standard normal. We assume that both population distributions are approximately normal with unknown standard deviations. What is the value of the sample test statistic? (Test the difference #₁ #₂. Round your answer to two decimal places.) *** (c) Find (or estimate) the P-value. (Round your answer to four decimal places.)
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:Education influences attitude and lifestyle. Differences in education are a big factor in the "generation gap." Is the younger generation really better educated? Large
surveys of people age 65 and older were taken in n₁ = 34 U.S. cities. The sample mean for these cities showed that x₁ = 15.2% of the older adults had attended
college. Large surveys of young adults (age 25 - 34) were taken in n₂ = 31 U.S. cities. The sample mean for these cities showed that x₂ = 19.1% of the young adults
had attended college. From previous studies, it is known that ₁ = 6.2% and ₂ = 4.4%. Does this information indicate that the population mean percentage of young
adults who attended college is higher? Use a = 0.05.
(a) What is the level of significance?
State the null and alternate hypotheses.
o Hoi H = Hi Hi Hi th
O Ho 1 = Hzi H1: H1 <H2
O Ho H₁ H₂ H ₂₁: M₁ = M₂
O Ho: M₁ = H₂i Hqi Hy > H₂
(b) What sampling distribution will you use? What assumptions are you making?
O The Student's t. We assume that both population distributions are approximately normal with unknown standard deviations.
O The standard normal. We assume that both population distributions are approximately normal with known standard deviations.
O The Student's t. We assume that both population distributions are approximately normal with known standard deviations.
O The standard normal. We assume that both population distributions are approximately normal with unknown standard deviations.
What is the value of the sample test statistic? (Test the difference ₁-₂. Round your answer to two decimal places.)
(c) Find (or estimate) the P-value. (Round your answer to four decimal places.)
Transcribed Image Text:AM
P-value
Sketch the sampling distribution and show the area corresponding to the P-value.
LA
P-value
0
z
0
0
2
P-value
P-value
2
(d) Based on your answers in parts (a) to (c), will you reject or fail to reject the null hypothesis? Are the data statistically significant at level a?
O At the a = 0.05 level, we reject the null hypothesis and conclude the data are statistically significant.
O At the a = 0.05 level, we fail to reject the null hypothesis and conclude the data are statistically significant.
O At the a = 0.05 level, we fail to reject the null hypothesis and conclude the data are not statistically significant.
O At the a= 0.05 level, we reject the null hypothesis and conclude the data are not statistically significant.
(e) Interpret your conclusion in the context of the application.
O Fail to reject the null hypothesis, there is insufficient evidence that the mean percentage of young adults who attend college is higher.
O Reject the null hypothesis, there is sufficient evidence that the mean percentage of young adults who attend college is higher.
O Reject the null hypothesis, there is insufficient evidence that the mean percentage of young adults who attend college is higher.
O Fail to reject the null hypothesis, there is sufficient evidence that the mean percentage of young adults who attend college is higher.
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