Answer:
Null hypothesis: H0; P = 0.75
Alternative hypothesis: Ha; P ≠ 0.75
z = -2.55
P value = P(Z<-2.556) + P(Z>2.556) = 0.011
Decision: We FAIL to REJECT the null hypothesis
Can we conclude that the proportion of high school seniors who believe that "getting rich" is an important goal has changed = NO
Rule
If;
P-value > significance level --- accept Null hypothesis
P-value < significance level --- reject Null hypothesis
Z score > Z(at 99% confidence interval) ---- reject Null hypothesis
Z score < Z(at 99% confidence interval) ------ accept Null hypothesis
Step-by-step explanation:
Given;
n= 250 represent the random sample taken
Null hypothesis: H0; P = 0.75
Alternative hypothesis: Ha ≠ 0.75
Test statistic z score can be calculated with the formula below;
z = (p^−po)/√{po(1−po)/n}
Where,
z= Test statistics
n = Sample size = 250
po = Null hypothesized value = 0.75
p^ = Observed proportion = 170/250 = 068
Substituting the values we have
z = (0.68-0.75)/√(0.75(1-0.75)/250)
z = −2.556
To determine the p value (test statistic) at 0.01 significance level, using a two tailed hypothesis.
P value = P(Z<-2.556) + P(Z>2.556) = 0.011
Since z at 0.01 significance level is between -2.58 and +2.58 and the z score for the test (z = -2.556) which doesn't falls with the region bounded by Z at 0.01 significance level. And also the two-tailed hypothesis P-value is 0.011 which is lower than 0.01. Then we can conclude that we don't have enough evidence to reject the null hypothesis, and we can say that at 1% significance level the null hypothesis is valid, therefore we fail to reject the null hypothesis.
