Question

1. .We are interested in the average dollar amount lost by victims by burglary. The National Insurance Association has reported that the mean dollar amount lost by victims of burglary is $2,222. Assume that this is the population mean. We believe that the true population mean loss is different from this. Formally state the null and research hypotheses we would test to investigate this question. What if we believed the dollar amount to be higher?

2. A friend of yours claims that 20% of the people in your neighborhood have been the victim of a crime. Take this as your population value. You take a random sample of 60 homes and find that about 31% of the homes reported some kind of crime. Test the null hypothesis that the population proportion is 20% against the alternative that it is different from 20%. Set your alpha level at .05.

Answer 1

1)
Below are the null and alternative Hypothesis,
Null Hypothesis, H0: μ = 2222
Alternative Hypothesis, Ha: μ > 2222

b)
Below are the null and alternative Hypothesis,
Null Hypothesis, H0: p = 0.2
Alternative Hypothesis, Ha: p ≠ 0.2

Rejection Region
This is two tailed test, for α = 0.05
Critical value of z are -1.96 and 1.96.
Hence reject H0 if z < -1.96 or z > 1.96

Test statistic,
z = (pcap - p)/sqrt(p*(1-p)/n)
z = (0.31 - 0.2)/sqrt(0.2*(1-0.2)/60)
z = 2.13

P-value Approach
P-value = 0.0332
As P-value < 0.05, reject the null hypothesis.