Question

It is commonly thought that very few U.S. adults believe in reincarnation (the rebirth of a soul in a new body). But a researcher thinks that group has been growing and wants to convince others that the percentage who believe in reincarnation is greater than 20%. In the researcher’s random sample of 942 U.S. adults, 195 stated that they believe in reincarnation. Does the researcher’s sample provide sufficient evidence to support the idea that more than 20% of all U.S. adults believe in reincarnation? Show the complete testing process and always include your statistical output.

Answer 1

Solution :

Given that,

= 0.20

Po

1 - = 0.80

Po

n = 942

x = 195

Level of significance = $\alpha$ = 0.05

Point estimate = sample proportion = $\hat p$ = x / n = 0.207

This a right (One) tailed test.

The null and alternative hypothesis is,

Ho: p = 0.20

Ha: p 0.20

Test statistics

z = ($\hat p$ -
Po
) / $\sqrt{}$
Po
*(1-
Po
) / n

= ( 0.207 - 0.20) / $\sqrt{}$ (0.20*0.80) /942

= 0.538

Critical value of  the significance level is α = 0.05, and the critical value for a right-tailed test is

$Z_{c}$ = 1.64

Since it is observed that z = 0.538 < $Z_{c}$ = 1.64, it is then concluded that the null hypothesis is fail to rejected.

P-value = P(Z>z)

= 1 - P(Z <z )

= 1- P(Z < 0.538)

= 0.2954

The p-value is p = 0.2954, and since p = 0.2954 < 0.05, it is concluded that the null hypothesis is fail to rejected.

Conclusion:

There is not sufficient evidence to support the idea that more than 20% of all U.S. adults believe in reincarnation.