Answer:
Given:
Sample size, n = 120
P = 48% = 0.48
p' = [tex]\frac{48}{120}[/tex]= 0.4
Significance level = 0.10
Null and alternative hypotheses are:
H0 : P = 0.48
H1 : P ≠ 0.48
For the test statistics:
[tex] Z = \frac{p' - P}{\sqrt{\frac{P(1 - P)}{n}}} [/tex]
[tex] Z = \frac{0.40 - 0.48}{\sqrt{\frac{0.48(1 - 0.48)}{120}}} [/tex]
Z = -1.754
P-value: This is a two tailed test.
For Z = -1.754 the P-value = 0.7943
Critical value: a = 0.10, 2 tailed test, Z critical = +1.645, -1.645
Decision Rule: We reject H0, if pvalue is less than significance level. We also reject H0 is Z observed is greater than Z critical.
Decision: Since pvalue, 0.7943 is greater than significance level, 0.10 we fail to reject null hypothesis, H0.
Conclusion:
There is not enough sufficient evidence to conclude that percentage of people who believe there is life on other planets differs from 48%
