Question

Suppose BC Ministry of Labor wants to condust a research on the percentage of young people who want to move from BC to look for a job. For this reason, they conducted a survey to see if the percentage of people willing to move is bigger than 60%. Of 1000 respondebts , 61% reported that they preferred to look for a job in a different province rather than BC.

a. State the null and alternative hypothesis. You can use the symbols tab (after Q5) to copy the symbols you need.

H0:

HA:

b. At the 0.05 level of significance, is there evidence that the proportion of all jobseekers who preferred to move out of BC is bigger than 60%? Show all the steps!

Answer 1

a) Null Hypothesis H0; p = 0.60

Alternative Hypothesis H1: p > 0.60 ( Right Tailed Test)

b) The sample proportion is $\widehat{p} = 0.61$

Num ber of respondents ( Sample Size) n = 1000

Under H0, the test statistic is

$Z=\frac{\widehat{p}-p}{\sqrt{pq/n}} =\frac{0.61-0.60}{\sqrt{0.60*0.40/1000}}=0.646$

Significance Level $\alpha = 0.05$

The critical value of Z for 5% significance level is 1.645

Decision Rule : Reject H0 , if Z> 1.645

The P-Value is 0.2591

Since Z calculated is less than Z tabulated, Fail to Reject H0.

Hence, at 5% significance level, we do not have enough evidence that the proportion of all jobseekers who preferred to move out of BC is bigger than 60%