Answer:
We conclude that older people are more likely to be victimized.
Step-by-step explanation:
We are given that a survey shows that 10% of the population is victimized by property crime each year.
A random sample of 527 older citizens (65 years or more of age) shows a victimization rate of 12.35%
Let p = <u><em>population proportion of people who are victimized</em></u>.
So, Null Hypothesis, :
10% {means that older people are less likely to be victimized or remains same}
Alternate Hypothesis, : p > 10% {means that older people are more likely to be victimized}
The test statistics that would be used here <u>One-sample z-test for</u> <u>proportions</u>;
T.S. = ~ N(0,1)
where, = sample proportion of older people who are victimized = 12.35%
n = sample of older citizens = 527
So, <u><em>the test statistics</em></u> =
= 1.798
The value of z-test statistics is 1.798.
Since in the question, we are not given with the level of significance so we assume it to be 5%. Now at 5% level of significance, the z table gives a critical value of 1.645 for right-tailed test.
Since our test statistics is more than the critical value of z as 1.798 > 1.645, so we have sufficient evidence to reject our null hypothesis as it will fall in the rejection region.
Therefore, we conclude that older people are more likely to be victimized.
