14:40 LTE 1 n3 1 A student wants to test the null hypothesis that the mean of so

Question

14:40 LTE 1 n3 1 A student wants to test the null hypothesis that the mean of some normal population is zero versus the two-sided alternative using a sample of size 9. It is known that the population standard deviation is 50. 1. What will be the acceptance region for the z-statistic of this test if he's going to use a 3% significance test? write it as two numbers separated by a comma. -108.50452,108.50452 (1 point) Incorrect 2. The following sample was obtained from this distribution: 57, -22, -38, -18, 38, -56, -72, -173, -6 What is the value of the z-statistic? 1.932 Correct 3. What is the p-value of the test? (1 point) 0.9691774 (1 point) Incorrect

Explanation / Answer

Solution1:

alpha=1-0.97

alpha=0.03

alpha/2=0.03/2=0.015

using ti83

vars>2nd>invnorm

enter

invnorm(0.015)

we get -2.1701 and 2.1701

ANSWER:-2.17,2.17

Solution2:

z=sample mean-population mean/population stddev/sqrt(n)

z=x-mean/sd/sqrt(n)

=-32.22222-0/50/sqrt(9)

=-32.22222/50/3

Z =1.933

ANSWER:Z:1.933

Solution3:

For z=-1.933

USING R CODE:

2*pnorm(-1.933)

p=0.0532

ANSWER:0.0532

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