In the 2016 fiscal year (FY), 78.1% of all convicted offenders were sentenced to incarceration (table 5.3). However, 86.6% of the 28,734 convicted offenders that had less than a high school diploma were sentenced to incarceration. Test the claim that the percent of convicted offenders with less than high school diploma is not the same as the percentage of the overall population of convicted offenders using = .05. (hint: x = p-hat * n, round mathematically)

What are the hypotheses?

a.

H0: p = .781

H1: p .781

b.

H0: p = .781

H1: p < .781

c.

H0: p = .781

H1: p > .781

d.

H0: p = .866

H1: p .866

e.

H0: p = .866

H1: p < .866

f.

H0: p = .866

H1: p > .866

What type of test is this?

a.

T-test for Pop. Proportion

b.

T-test for Mean

c.

Z-test for Mean

d.

Chi Test for Std Dev.

What is the test statistic? Round the hundredths

What is the p-value?

In the 2016 fiscal year (FY), nationwide the mean incarceration sentence length for drug offenses was 75 months (table 5.4). However, Black/African Americans served a mean sentence length of 83.6 months. Assuming a standard deviation of 11 months (figure 2) from a study of 1112 cases, test the claim that B/AA serve terms that are greater than the national mean of 75 months using = .05. (hint: s = 11)

What are the hypotheses?

a.

H0: =75=75

H1: >75>75

b.

H0:=75=75

H1: 7575

c.

H0:=75=75

H1: <75<75

d.

H0: =83.6=83.6

H1:>83.6>83.6

e.

H0: =83.6=83.6

H1: <83.6<83.6

f.

H0: =83.6=83.6

H1: 83.6

What type of test is this?

a.

T-test for Pop. Proportion

b.

T-test for Mean

c.

Z-test for Mean

d.

Chi Test for Std Dev.

What is the test statistic? Round to the hundredths.

What is the p-value?

In FY2010, the nationwide mean incarceration sentence for weapon offenses was 73.8 months (table 5.4). However, women served a mean sentence of 52.7 months. We will assume the population standard deviation for all cases was 38 months (pg. 248). Approximately 901 women (13.7% of convictions were women and there were 6575 convicted weapon offense) received weapons offense sentences in FY2016. Test the claim that women serve a sentence that is less than the national mean of 84 months using = .05. (hint: = 38, I had to take some liberties here bc I couldn't find the std. dev.).

What are the hypotheses?

a.

H0: =73.8=73.8

H1: <73.8<73.8

b.

H0: =73.8=73.8

H1: >73.8>73.8

c.

H0: =73.8=73.8

H1: 73.873.8

d.

H0: =52.7=52.7

H1: 52.752.7

e.

H0: =52.7=52.7

H1: <52.7<52.7

f.

H0: =52.7=52.7

H1: >52.7>52.7

What is the test statistic? Round the hundredths.

What's the p-value?

The study explored the mean sentence lengths and standard deviation of sentences of cases that followed guidelines and for those who did not. In 967 cases, guidelines were followed. Those cases had a standard deviation of 3.92 months (p. 40). Assuming the population standard deviation for all cases of the same nature was 11 months, test the claim that the standard deviation for the 967 guideline cases is less than the population standard deviation of 11 months with = .025 (use df = 950).

What are the hypotheses?

a.

H₀: = 11

H_{1 :} 11

b.

H₀: = 11

H_{1 :} < 11

c.

H₀: = 11

H_{1 :} > 11

d.

H₀: = 3.92

H_{1 :} 3.92

e.

H₀: = 3.92

H_{1 :} > 3.92

f.

H₀: = 3.92

H_{1 :} < 3.92

What type of test is this?

a.

T-test for Pop. Proportion

b.

Z-test for Mean

c.

T-test for Mean

d.

Chi Test for Std Dev.

What is the test statistic? Round to the hundredths.

What is the p-value OR the critical value?

Either is fine, but do NOT put both! For the critical, but the full value from the chart. https://www.medcalc.org/manual/chi-square-table.php