Question

Let X be the population of house prices in a large city. Assume that the population distribution of house prices is normal [i.e., X ~ N(μ, σ2)]. A random sample of 10 house prices (in thousands of $) provided the following data:

      90    100   115   72    125   95    105   135   120   88

1. Find the standard error of the sample mean (?̅). Show your calculations.

2. Write out the null and alternative hypotheses for determining whether the population mean

   differs from 90 (thousand $).

3. Write out the decision rule for the question in (b).

4. Find the calculated test-value for the question in (b). Show your calculations.

5. Find the 10%, 5%, and 1% critical values for the question in (b).

6. Do you reject the null hypothesis in (b)? Explain clearly.

7. The p-value for the question in (b) is 0.041. What does the p-value mean, and how does it

   change your conclusion in (f)? Explain clearly.

Answer 1

ANSWER::

(a)

n = 10

=1045/10 = 104.5

x	x -	(x - )2
90	-14.5	210.25
100	-4.5	20.25
115	10.5	110.25
72	-32.5	1056.25
125	20.5	420.25
95	-9.5	90.25
105	0.5	0.25
135	30.5	930.25
120	15.5	240.25
88	-16.5	272.25
Total =		3350.5

Standard Error is given by:

SE = s/

= 19.2945/

= 6.1015

So,

Answer is:

6.1015

(b)

H0: Null Hypothesis: =90

HA: Alternative Hypothesis: 90

(c)

Decision Rule:

Reject H0 if tO < - tC OR tO > tC,

where

tO is observed test statistic

tC is the critical value

(d)

Test Statistic is given by:

So,

Test Statistic is 2.376

(e)

df = 10 - 1 = 9

From Table:

10% critical values: 1.833

5% critical values: 2.262

1% critical values: 3.250

(f)

For = 0.10, since calculated value of t = 2.376 is greater than critical value of t = 1.833, Reject the null hypothesis in (b)

For = 0.05, since calculated value of t = 2.376 is greater than critical value of t = 2.262, Reject the null hypothesis in (b)

For = 0.01, since calculated value of t = 2.376 is less than critical value of t = 3.250, Fail to reject the null hypothesis in (b)

(g)

For = 0.10, since p value = 0.041 is less than = 0.05 , Reject the null hypothesis in (b)

For = 0.05, since p value = 0.041 is less than = 0.05 , Reject the null hypothesis in (b)

For = 0.01, since p value = 0.041 is greater than = 0.01 , Fail to reject the null hypothesis in (b)

It does not change our conclusion.

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