Question

7. The claim is that the proportion of adults who smoked a cigarette in the past week is less than 0.30​, and the sample statistics include n=1181subjects with 331 saying that they smoked a cigarette in the past week. Find the value of the test statistic.

The test statistics is____

​(Round to two decimal places as​ needed.)

8. The claim is that the IQ scores of statistics professors are normally​ distributed, with a mean greater than greater than 127 A sample of 20 professors had a mean IQ score of 128 with a standard deviation of 7. Find the value of the test statistic.

The value of the test statistic is____

(Round to three decimal places as​ needed.)

9. Assume that the significance level is α=0.05. Use the given information to find the​ P-value and the critical​ value(s).The test statistic of z=1.91 is obtained when testing the claim that p>0.2.

P-value= ____

​(Round to four decimal places as​ needed.)

The critical​ value(s) is/are z=_____

​(Round to two decimal places as needed. Use a comma to separate answers as​ needed.)

Answer 1

Solution :

Given that,

7)

= 0.30

1 - = 1 - 0.30 = 0.70

n = 1181

x = 331

Point estimate = sample proportion = = x / n = 331 / 1181 = 0.280

The test statistics

z = ( - ) / *(1-) / n

= ( 0.280 - 0.30) / (0.30*0.70) / 1181

= -1.50

8)

Solution :

Given that,

Population mean = = 127

Sample mean = = 128

Sample standard deviation = s = 7

Sample size = n = 20

The test statistics,

t = ( - )/ (s/)

= (128 - 127) / ( 7 / 20)

= 0.639

9)

z = 1.91

This is a right tailed test.

p-value = P(Z > z )

= 1 - P(Z < 1.91)

= 1 - 0.9719

= 0.0281

= 0.05

The critical value of z is,

z = 1.65