Question

The population of cities in the United States reports 30 crimes per hour. A researcher believes that regions lower in socioeconomic status will have more crimes per hour. A sample of cities crimes per hour are listed below. Compare these scores to the population (? = .05).

Cities low in SES	Crimes per hour
1	24
2	32
3	29
4	31
5	33
6	34
7	31
8	32
9	30
10	30

Will we need a one- or two-tailed hypothesis test?

State your null hypothesis

State your alternative hypothesis

Provide e t-obtained and the p-value

Did you reject or fail to reject the null hypothesis?

What can you conclude?

Calculate the 95% confidence interval for the sample mean

Calculate the 95% confidence interval for the difference between the means

Calculate Cohen’s d

Answer 1

Solution:-

State the hypotheses. The first step is to state the null hypothesis and an alternative hypothesis.

Null hypothesis: u < 30
Alternative hypothesis: u > 30

Note that these hypotheses constitute a one-tailed test. The null hypothesis will be rejected if the sample mean is too small.

Formulate an analysis plan. For this analysis, the significance level is 0.01. The test method is a one-sample t-test.

Analyze sample data. Using sample data, we compute the standard error (SE), degrees of freedom (DF), and the t statistic test statistic (t).

SE = s / sqrt(n)

S.E = 0.87178
DF = n - 1

D.F = 9
t = (x - u) / SE

t = 0.688

where s is the standard deviation of the sample, x is the sample mean, u is the hypothesized population mean, and n is the sample size.

The observed sample mean produced a t statistic test statistic of 0.688.

Thus the P-value in this analysis is 0.254

Interpret results. Since the P-value (0.254) is greater than the significance level (0.05), we cannot reject the null hypothesis.

From the above test we do not have sufficient evidence in the favor of the claim that regions lower in socioeconomic status will have more crimes per hour.

95% confidence interval for the sample mean is C.I = (28.627, 32.573).

C.I = 30.6 + 2.263 × 0.87178

C.I = 30.6 + 1.97284

C.I = (28.627, 32.573)