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Forty-six percent of people believe that there is life on other planets in the universe. A scientist does not agree with this finding. He surveyed 120 randomly selected individuals and found 48 believed that there is life on other planets.
(a) At α = 0.10, is there sufficient evidence to conclude that the percentage differs from 48?

Respuesta :

Chrisnando

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%

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