In 2006 the median home price in Orange County was $650,000. The sample mean hom

Question

In 2006 the median home price in Orange County was $650,000.

The sample mean home price in 2014 was $648,000 with a sample

variance of $800,000 for a random sample of 35 homes.

Using this information and alpha = .05, can we conclude that the

average home price in Ventura County is different from $650,000?

What is the correct hypothesis test?

Conduct the hypothesis test in question. Do you accept or reject the null hypothesis?

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Last year the average GPA of all students is 3.25. You randomly sample 55 students and calculate a sample mean of 3.33. Assume the population

variance is 1.95 and alpha = .07. Can you conclude that average GPA has increaed at this school?

What is the correct hypothesis test?

Do you accept or reject the null hypothesis?

Explanation / Answer

Question 1 : x home price = $648000 , s2 = 800000

Null HYpothesis : H0 : home price = $ 65000

ALternative Hypothesis : Ha : home price $ 65000

so the correct hypothesis is to check whether there is change in home prioce in 2014 from $ 650000

Test statistic : t = (x home price - $650000)/ sqrt (s2 /n) = 2000/ sqrt( 800000/35) = 13.23

andfor significance level alpha = 0.05 => t (critical) = 2.03

so, here we can reject the null hypothesis as t critical < t, so we can conclude that there is significant difference between home prices in 2014 from 2006.

Question 2. xsample = 3.33 , n = 55

= 3.25 and = 1.95 and alpha = 0.07

Null HYpothesis : H0 : cgpa this year = cgpa last year

ALternative Hypothesis : Ha : cgpa this year   > cgpa last year

so this is the correct hypotheis and as population variance is given we can use ONE- Tailed z- test

Test statistic : Z = (xsample -  3.25)/ sqrt (2 /n) = (3.33 - 3.25)/ sqrt( 1.95/55) = 0.08/ 0.1828 = 0.425

andfor significance level alpha = 0.07 => z (critical) = 1.475

so, here we cannot reject the null hypothesis as z critical > z , so we can conclude that there is no significant difference between cgpa this year and cggpa last year.

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