2. Some defendants in criminal proceedings plead guilty and are sentenced without a trial, whereas others who plead innocent are subsequently found guilty and then are sentenced. In recent years, legal scholars have speculated as to whether sentences of those who plead guilty differ in severity from sentences for those who plead innocent and are subsequently judged guilty. Consider the data given below on defendants accused of robbery, all of whom, by the way, had previous prison records. At the .01 level of significance, do these data suggest that the proportion of all defendants in these circumstances who plead guilty and are sent to prison differs from the proportion who are sent to prison after pleading innocent and being found guilty?

Plea

Guilty Not Guilty

Number judged guilty n1 = 191 n2 = 64

Number sentenced to prison x1 = 101 x2 = 56

Sample proportion

A. No, because the test value -1.96 is inside the interval (-2.58, 2.58)

B. No, because the test value -4.94 is outside the interval (-1.96, 1.96)

Yes, because the test value -4.94 is outside the interval (-2.58, 2.58)

D. Yes, because the test value 2.58 is inside the interval (-4.94, 4.94)

Serum ferritin is used in diagnosing iron deficiency. In a study conducted recently researchers discovered that in a sample of 28 elderly men the sample standard deviation of serum ferritin was 52.6 mg/L. For 26 younger men the sample standard deviation was 84.2 mg/L. At the .01 level of significance, do these data support the conclusion that the ferritin distribution in elderly men has a smaller variance than in younger men?

A. No, because the test value 1.60 is less than the critical value of 2.54

B. Yes, because the test value 2.56 is greater than the critical value of 2.54

C. Yes, because the test value 0.390 is less than the critical value 2.54

D. Yes, because the test value 2.56 is greater than the critical value 0.394

The data presented in the table below resulted from an experiment in which seeds of 5 different types were planted and the number of seeds that germinated within 5 weeks after planting was recorded for each seed type. At the .01 level of significance, is the proportion of seeds that germinate dependent on the seed type?

Seed Type Observed Frequencies

Germinated Failed to Germinate

1 31 7

2 57 33

3 87 60

4 52 44

5 10 19

A. Yes, because the test value 16.86 is greater than the critical value of 13.28

B. Yes, because the test value 16.86 is less than the critical value of 14.86

C. No, because the test value 16.86 is greater than the critical value of 13.28

D. No, because the test value 13.28 is less than the critical value of 16.86

Plea

Guilty Not Guilty

Number judged guilty n1 = 191 n2 = 64

Number sentenced to prison x1 = 101 x2 = 56

Sample proportion

A. No, because the test value -1.96 is inside the interval (-2.58, 2.58)

B. No, because the test value -4.94 is outside the interval (-1.96, 1.96)

Yes, because the test value -4.94 is outside the interval (-2.58, 2.58)

D. Yes, because the test value 2.58 is inside the interval (-4.94, 4.94)

Serum ferritin is used in diagnosing iron deficiency. In a study conducted recently researchers discovered that in a sample of 28 elderly men the sample standard deviation of serum ferritin was 52.6 mg/L. For 26 younger men the sample standard deviation was 84.2 mg/L. At the .01 level of significance, do these data support the conclusion that the ferritin distribution in elderly men has a smaller variance than in younger men?

A. No, because the test value 1.60 is less than the critical value of 2.54

B. Yes, because the test value 2.56 is greater than the critical value of 2.54

C. Yes, because the test value 0.390 is less than the critical value 2.54

D. Yes, because the test value 2.56 is greater than the critical value 0.394

The data presented in the table below resulted from an experiment in which seeds of 5 different types were planted and the number of seeds that germinated within 5 weeks after planting was recorded for each seed type. At the .01 level of significance, is the proportion of seeds that germinate dependent on the seed type?

Seed Type Observed Frequencies

Germinated Failed to Germinate

1 31 7

2 57 33

3 87 60

4 52 44

5 10 19

A. Yes, because the test value 16.86 is greater than the critical value of 13.28

B. Yes, because the test value 16.86 is less than the critical value of 14.86

C. No, because the test value 16.86 is greater than the critical value of 13.28

D. No, because the test value 13.28 is less than the critical value of 16.86

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