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A researcher wants to test if the mean price of houses in an area is greater than $145,000. Suppose we make the test at the 2% significance level. A sample of 36 houses selected from this area produces a mean price of $149,750 and a standard deviation of $24,600. What is the value of the test statistic?

Respuesta :

Answer:

The value of the test statistic is 1.158.

Step-by-step explanation:

We are given that a researcher wants to test if the mean price of houses in an area is greater than $145,000.

A sample of 36 houses selected from this area produces a mean price of $149,750 and a standard deviation of $24,600.

Let [tex]\mu[/tex] = mean price of houses in an area.

SO, Null Hypothesis, [tex]H_0[/tex] : [tex]\mu \leq[/tex]  $145,000   {means that the mean price of houses in an area is smaller than or equal to $145,000}

Alternate Hypothesis, [tex]H_A[/tex] : [tex]\mu[/tex] > $145,000   {means that the mean price of houses in an area is greater than $145,000}

The test statistics that will be used here is One-sample t test statistics as we don't know about the population standard deviation;

                      T.S.  = [tex]\frac{\bar X -\mu}{\frac{s}{\sqrt{n} } }[/tex]  ~ [tex]t_n_-_1[/tex]

where, [tex]\bar X[/tex] = sample mean price of houses selected = $149,750

             s = sample standard deviation = $24,600

             n = sample of houses = 36

So, test statistics  =  [tex]\frac{149,750-145,000}{\frac{24,600}{\sqrt{36} } }[/tex]  ~ [tex]t_3_5[/tex]     

                               =  1.158

The value of the test statistic is 1.158.

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