Question

In: Statistics and Probability

A recent article in a local magazine indicated that the mean selling price of homes in...

A recent article in a local magazine indicated that the mean selling price of homes in the area is less than $232,000. Can we conclude that the mean selling price in the area is less than $232,000? Use the 0.01 significance level. {Use 232.0 as the value, not 232,000.}

Assume the list is a sample.

Price
263.1
182.4
242.1
213.6
139.9
245.4
327.2
271.8
221.1
266.6
292.4
209
270.8
246.1
194.4
281.3
172.7
207.5
198.9
209.3
252.3
192.9
209.3
345.3
326.3
173.1
187
257.2
233
180.4
234
207.1
247.7
166.2
177.1
182.7
216
312.1
199.8
273.2
206
232.2
198.3
205.1
175.6
307.8
269.2
224.8
171.6
216.8
192.6
236.4
172.4
251.4
246
147.4
176
228.4
166.5
189.4
312.1
289.8
269.9
154.3
222.1
209.7
190.9
254.3
207.5
209.7
294
176.3
294.3
224
125
236.8
164.1
217.8
192.2
125.9
220.9
294.5
244.6
199
240
263.2
188.1
243.7
221.5
175
253.2
155.4
186.7
179
188.3
227.1
173.6
188.3
310.8
293.7
179
188.3
227.1
173.6
188.3

Requirement following the hypotheses testing 6-step process:

State Null and Alternative Hypotheses,
State the significance level.
State which distribution is used.
State the decision rule including graph.
State the test statistic and the p-value.
State the conclusion.

Notes:

Use 232.0 instead of 232,000.
State z-values to 2 decimal places unless 3 decimal places are needed; State t-values to 3 decimal places; State p-values to 4 decimal places.

Expert Solution

using excel>Addin>phstat>one sample test

we have

t Test for Hypothesis of the Mean

Data
Null Hypothesis m=	232
Level of Significance	0.01
Sample Size	105
Sample Mean	221.1028571
Sample Standard Deviation	47.10540443

Intermediate Calculations
Standard Error of the Mean	4.597016762
Degrees of Freedom	104
t Test Statistic	-2.370481428

Lower-Tail Test
Lower Critical Value	-2.362739201
*p-Value*	0.009803774
Reject the null hypothesis

1 ) the Null and Alternative Hypotheses are

Ho: u = 232

Ha: u <232 ( one tailed )

2 ) the significance level is 0.01

3 ) we will use t distribution because sigma is unknown

4 ) the value of test stat t at 0.01 with 104 df is -2.363

we will reject Ho if t < -2.263

5 )the test statistic t =-2.371

and the p-value. is 0.0098

6 ) conclusion. : since p value is less than so we reject Ho and conclude that mean selling price in the area is less than $232,000

orchestra answered 1 year ago

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