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 = 30 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 = 34 U.S. cities. The sample mean for these cities showed that x₂ = 19.7% of the young adults had attended college. From previous studies, it is known that ?₁ = 6.8% and ?₂ = 4.8%. Does this information indicate that the population mean percentage of young adults who attended college is higher? Use ? = 0.05.

I need help with finding the P-value
Transcribed Image Text:Sketch the sampling distribution and show the area corresponding to the P-value. b a P.value P-value d P-value P-value -z -z (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 fail to reject the null hypothesis and conclude the data are not statistically significant. At the a = 0.05 level, we reject the null hypothesis and conclude the data are not 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 reject the null hypothesis and conclude the data are statistically significant. (e) Interpret your conclusion in the context of the application. O Fail to 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 sufficient evidence that the mean percentage of young adults who attend college is higher. 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 insufficient evidence that the mean percentage of young adults who attend college is higher.
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 n, = 30 U.S. cities. The sample mean for these cities showed that x, = 15.2% of the older adults had attended college. Large surveys of young adults (age 25 - 34) were taken in n, = 34 U.S. cities. The sample mean for these cities showed that x, = 19.7% of the young adults had attended college. From previous studies, it is known that o, = 6.8% ando, = 4.8%. 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 Ho: H1 = H2i Hz: H1 < Hz O Ho: H1 = H2i Hi: Hy # Hz O Ho: H1 < Hzi Hi: H1 = H2 O Ho: H1 = H2i H;: H1 > Hz (b) What sampling distribution will you use? What assumptions are you making? 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 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 unknown standard deviations. What is the value of the sample test statistic? (Test the difference u, - µz. Round your answer to two decimal places.) (c) Find (or estimate) the P-value. (Round your answer to four decimal places.)

Question

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 = 30 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 = 34 U.S. cities. The sample mean for these cities showed that x₂ = 19.7% of the young adults had attended college. From previous studies, it is known that ?₁ = 6.8% and ?₂ = 4.8%. Does this information indicate that the population mean percentage of young adults who attended college is higher? Use ? = 0.05.

I need help with finding the P-value

Sketch the sampling distribution and show the area corresponding to the P-value.
b
a
P.value
P-value
d
P-value
P-value
-z
-z
(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 fail to reject the null hypothesis and conclude the data are not statistically significant.
At the a = 0.05 level, we reject the null hypothesis and conclude the data are not 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 reject the null hypothesis and conclude the data are statistically significant.
(e) Interpret your conclusion in the context of the application.
O Fail to 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 sufficient evidence that the mean percentage of young adults who attend college is higher.
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 insufficient evidence that the mean percentage of young adults who attend college is higher.

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 n, = 30 U.S. cities. The sample mean for these
cities showed that x, = 15.2% of the older adults had attended college. Large surveys of young adults (age 25 - 34) were taken in n, = 34 U.S. cities. The sample mean for these cities showed that x, = 19.7% of the young adults had attended college. From
previous studies, it is known that o, = 6.8% ando, = 4.8%. 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 Ho: H1 = H2i Hz: H1 < Hz
O Ho: H1 = H2i Hi: Hy # Hz
O Ho: H1 < Hzi Hi: H1 = H2
O Ho: H1 = H2i H;: H1 > Hz
(b) What sampling distribution will you use? What assumptions are you making?
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 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 unknown standard deviations.
What is the value of the sample test statistic? (Test the difference u, - µz. Round your answer to two decimal places.)
(c) Find (or estimate) the P-value. (Round your answer to four decimal places.)

Accepted Answer

The test statistic is,
z=x¯1-x¯2σ12n1+σ22n2=15.2-19.76.8230+4.8234=-4.51.48962424529=-3.0209≈-3.02…