Question

One urban affairs sociologist claims that the proportion,

p

, of adult residents of a particular city who have been victimized by a criminal is at least

55%

. A random sample of

245

adult residents of this city were questioned, and it was found that

119

of them had been victimized by a criminal. Based on these data, can we reject the sociologist's claim at the

0.05

level of significance?

Perform a one-tailed test. Then fill in the table below.

Carry your intermediate computations to at least three decimal places and round your answers as specified in the table.

The null hypothesis:	H0:
The alternative hypothesis:	H1:
The type of test statistic:	(Choose one)ZtChi squareF
The value of the test statistic: (Round to at least three decimal places.)
The critical value at the 0.05 level of significance: (Round to at least three decimal places.)
Can we reject the claim that the proportion of adult residents of the city who have been victimized by a criminal is at least 55% ?		Yes	No

Answer 1

Below are the null and alternative Hypothesis,
Null Hypothesis, H0: p = 0.55

Alternative Hypothesis, Ha: p < 0.55

The type of test statistic is single proportion z test

Test statistic,
z = (pcap - p)/sqrt(p*(1-p)/n)
z = (0.4857 - 0.55)/sqrt(0.55*(1-0.55)/245)
z = -2.023

Critical value of z is -1.645.
Hence reject H0 if z < -1.645

yes, we can reject the claim that the proportion of adult residents of the city who have been victimized by a criminal is at least
55%