Question

A researcher claims that more than 55% of adults believe it is very likely that life exists on other planets. In a survey of 1000 adults, 585 say it is very likely that life exists on other planets. At α = 0.05, can you support the researcher’s claim?

Answer 1

Solution:

Here, we have to use one sample z test for the population proportion.

The null and alternative hypotheses for this test are given as below:

Null hypothesis: H0: No more than 55% of adults believe it is very likely that life exists on other planets.

Alternative hypothesis: Ha: more than 55% of adults believe it is very likely that life exists on other planets.

H0: p ≤ 0.55 versus Ha: p > 0.55

This is an upper tailed test.

We are given

Level of significance = α = 0.05

Test statistic formula for this test is given as below:

Z = (p̂ - p)/sqrt(pq/n)

Where, p̂ = Sample proportion, p is population proportion, q = 1 - p, and n is sample size

x = number of items of interest = 585

n = sample size = 1000

p̂ = x/n = 585/1000 = 0.585

p = 0.55

q = 1 - p = 0.45

Z = (p̂ - p)/sqrt(pq/n)

Z = (0.585 – 0.55)/sqrt(0.55*0.45/1000)

Z = 2.2247

Test statistic = 2.2247

P-value = 0.0130

(by using z-table)

P-value < α = 0.05

So, we reject the null hypothesis

There is sufficient evidence to conclude that more than 55% of adults believe it is very likely that life exists on other planets.

We support the researcher’s claim.