A random sample of n1 = 148 people ages 16 to 19 were taken from the island of Oahu, Hawaii, and 14 were found to be high school dropouts. Another random sample of n2 = 125 people ages 16 to 19 were taken from Sweetwater County, Wyoming, and 5 were found to be high school dropouts. Do these data indicate that the population proportion of high school dropouts on Oahu is different (either way) from that of Sweetwater County? Use a 1% level of significance.
A random sample of n1 = 148 people ages 16 to 19 were taken from the island of Oahu, Hawaii, and 14 were found to be high school dropouts. Another random sample of n2 = 125 people ages 16 to 19 were taken from Sweetwater County, Wyoming, and 5 were found to be high school dropouts. Do these data indicate that the population proportion of high school dropouts on Oahu is different (either way) from that of Sweetwater County? Use a 1% level of significance.
MATLAB: An Introduction with Applications
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Author:Amos Gilat
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A random sample of n1 = 148 people ages 16 to 19 were taken from the island of Oahu, Hawaii, and 14 were found to be high school dropouts. Another random sample of n2 = 125 people ages 16 to 19 were taken from Sweetwater County, Wyoming, and 5 were found to be high school dropouts. Do these data indicate that the population proportion of high school dropouts on Oahu is different (either way) from that of Sweetwater County? Use a 1% level of significance.
Transcribed Image Text:A random sample of n, = 148 people ages 16 to 19 were taken from the island of Oahu, Hawaii, and 14 were found to be high school dropouts. Another random sample of n, = 125 people ages 16 to 19 were taken from Sweetwater County, Wyoming, and 5 were found to be high
school dropouts. Do these data indicate that the population proportion of high school dropouts on Oahu is different (either way) from that of Sweetwater County? Use a 1% level of significance.
n USE SALT
(a) What is the level of significance?
State the null and alternate hypotheses.
O Ho: P1 = P2i H: P1 <P2
O Ho: P1 = P2i H1: P1 > P2
O Ho: P1 = P2i H,i P1 * P2
O Ho: P1+ P2i HP1 = P2
(b) What sampling distribution will you use? What assumptions are you making?
O The standard normal. The number of trials is sufficiently large.
O The Student's t. We assume the population distributions are approximately normal.
O The Student's t. The number of trials is sufficiently large.
O The standard normal. We assume the population distributions are approximately normal.
What is the value of the sample test statistic? (Test the difference p, - p2. Do not use rounded values. Round your final answer to two decimal places.)
(c) Find (or estimate) the P-value. (Round your answer to four decimal places.)
Transcribed Image Text:Sketch the sampling distribution and show the area corresponding to the P-value.
a
b
O-3
-2
-1
1
2
O-3
-2
-1
2
d
C
-2
-1
1.
O-3
-2
-1
1
3
(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 = 0.01 level, we reject the null hypothesis and conclude the data are not statistically significant.
O At the a = 0.01 level, we fail to reject the null hypothesis and conclude the data are statistically significant.
O At the a = 0.01 level, we fail to reject the null hypothesis and conclude the data are not statistically significant.
O At the a = 0.01 level, we reject the null hypothesis and conclude the data are statistically significant.
(e) Interpret your conclusion in the context of the application.
O Reject the null hypothesis, there is sufficient evidence that the proportion of high-school dropouts on Oahu differs from that of Sweetwater County.
O Fail to reject the null hypothesis, there is sufficient evidence that the proportion of high-school dropouts on Oahu differs from that of Sweetwater County.
O Fail to reject the null hypothesis, there is insufficient evidence that the proportion of high-school dropouts on Oahu differs from that of Sweetwater County.
O Reject the null hypothesis, there is insufficient evidence that the proportion of high-school dropouts on Oahu differs from that of Sweetwater County.
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