Question

Rao's Finance claims that less than 50% of adults in Suva have a will. A will is a legal

Answer 1

Answer:

Step-by-step explanation:

Given:

Sample size, n= 1000

$X = \frac{450}{1000} = 0.45$

P' = 0.5

Level of significance, a = 0.05

a) The null and alternative hypotheses:

H0 : u ≥ 0.5

H1 : u < 0.5

This is a left tailed test.

Decision:

Reject null hypothesis H0 if p value is less than level of significance.

The test statistic, z =

$\frac{0.45 - 0.5}{0.5/ \sqrt{1000}}$

z = - 3.1623

From the standard normal table,

NORMSDIST(-3.1623)= 0.00078 ≈ 0.0008

Pvalue = 0.0008

Since p value, 0.0008 is less than significance level 0.05, we reject H0.

In conclusion, there is sufficient evidence to evidence to reject H0.

b) The type I error here is the claim that less than 50% of adults have a will, whereas the probability is not less than 50%.

Probability of type I error = significance level = 0.05

c)What would your decision be in part A if the probability of making a Type I error were zero?

If probability of making a type I error were zero in part A, we are to reject the null hypothesis, H0.