PLEASE HELP ME UNDERSTAND HOW TO SOLVE THIS QUESTION Independent random samples

Question

PLEASE HELP ME UNDERSTAND HOW TO SOLVE THIS QUESTION

Independent random samples of released prisoners in the fraud and firearms offense categories yielded the given information on time served, in months. At the 5% significance level, assuming the population variances are equal, do the data provide sufficient evidence to conclude that the mean time served for fraud is less than that for firearms offenses? Click the icon to view the data table showing the time served for each offense Let be the mean time served for fraud 2 the mean time served for firearms offenses. What are the correct hypotheses to test? Determine the p-value p-value-(Round to four decimal places as needed.) What is the conclusion of the hypothesis test? Since the P-value than that for firearms offenses | than . Ho. Conclude that the data sufficient evidence that the mean time served for fraud is less

Explanation / Answer

Since both sample sizes are less than 30

n1=10

n2=10

n1,n2<30

use t test for difference in means assuming equal variances

.

H0:mu1=mu2

H1:mu1<mu2

since it is clearly given to verify claim that the mean time served for fraud is less than that for firearms offenses.

OPTION C

Run t test for means assuming equal variances in excel.

p=0.0322

p<alpha

p value is less than alpha reject H0 .conclude that the data provides sufficient evidence that the mean time served for fraud is less than that for firearms offenses

t-Test: Two-Sample Assuming Equal Variances Fraud Firearms Mean 12.15 16.59 Variance 20.69611 30.07878 Observations 10 10 Pooled Variance 25.38744 Hypothesized Mean Difference 0 df 18 t Stat -1.97042 P(T<=t) one-tail 0.032185 t Critical one-tail 1.734064 P(T<=t) two-tail 0.064371 t Critical two-tail 2.100922

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