In a survey of 700 US adults with children, 270 of them reported that they saved money for their children’s college education. Can you conclude that more than one third (33%) of US adults with children have saved money for college? Use a 0.05 significance level.
a. State the null (H0) and alternative (H1) hypotheses.
b. Give the test statistics and the p-value for this significance test.
c. Make a decision on whether or not to reject the null hypothesis.
d. Summarize the conclusion in the context of this problem.
Solution :
This is the right tailed test .
The null and alternative hypothesis is ,
H0 : p = 0.33
Ha : p 0.33
n = 700
x = 270
= x / n = 270 / 700 = 0.3857
P0 = 0.33
1 - P0 = 1 - 0.33 = 0.67
z = - P0 / [P0 * (1 - P0 ) / n]
= 0.3857 - 0.33 / [(0.33 * 0.67) / 700]
= 3.135
This is the right tailed test .
P(z > 3.135) = 1 - P(z < 3.135) = 1 - 0.9991 = 0.0009
P-value = 0.0009
= 0.05
P-value <
Reject the null hypothesis .
one third (33%) of US adults with children have saved money for college .
In a survey of 700 US adults with children, 270 of them reported that they saved...
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