Question

QUESTION 13 A sample of 16 cookies is taken to test the claim that each cookie contains at least 9 chocolate chips. The average number of chocolate chips per cookie in the sample was 7.875. The standard deviation of the population is 2. Assume the distribution of the population is normal. Let u denote the average number of chocolate chips in all the cookies. The hypothesis to test the claim is: H: 129 Hu<9 The p-value for the test statistics is: a 0.0122 b. 0.0244 c 0.9878 d. 0.0139 3 poin QUESTION 14 Your instructor (Katie) believes that the average time of taking this exam is equal to 140 minutes. A sample of 4 students was taken and the following exam times were obtained. Assume the distribution of the population is normally distributed Sample: 150, 150, 180, 170 (Sample Std. Dev 15) The correct set of hypothesis is H. 140 and H,> 140 H 140 und H, 140 Click Save and Suwito wave and writ. Click Save All Arto e alla Me Books

Answer 1

13. Sample size = n = 16

Sample mean = = 7.875

X

Population standard deviation = $\sigma$ = 2

Population mean = $\mu$ = 9

Here we test for:

$H_0: \mu\geqslant 9$ v/s $H_1: \mu< 9$

We conduct the 1 sample Z test.

The test statistic Z is given by,

$Z= \frac{\sqrt n(\bar X-\mu)}{\sigma}$

$= \frac{\sqrt {16}(7.875-9)}{2}$

$= \frac{4*(-1.125)}{2}$

=-2.25

The p value ( left tailed ) is calculated using the p value calculator( specifying the value of the test statistic Z).

p value = 0.0122

ANS: The required p value is 0.0122

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