Paige M. answered • 05/31/20

College freshman tutor with experience in advanced mathematics

Hi, Julia! I hope this explanation helps you understand and answer your question.

IMPORTANT NOTE: For this problem, you would need to conduct a **two-sided** **z-test**, as opposed to a two-sided t-test. The main indicator for that is that the problem gives us the population standard deviation. The procedure you would typically follow may differ from mine, but I like to use the acronym, "PHANTOMS" when I conduct hypothesis tests. Define your **parameters. **State your **hypotheses**. **Assess** the conditions. **Name** the test. Calculate the **test statistic**. **Obtain** a P-value. **Make **a decision. **State **your conclusion in context.

a.) Your parameter would be defined by **μ**, which represents the **true mean home price, in thousands of dollars, for this year.** Your null hypothesis would be **μ = 260.7**, while your alternative hypothesis would be **μ≠ 260.7. **

b.) For this problem, the appropriate equation to use to calculate the z-statistic would be z = (x̅ - μ) / (σ/**√n). **Your sample mean x̅ is **290.5**, your population mean is **260.7**, your standard deviation σ is **150**, and your sample size n is **50**. Plug those numbers into the equation to get the z-statistic. You should get an answer of approximately **1.4048**.

c.) Using normalcdf (lower, upper, μ, σ ) on your graphing calculator, enter the following numbers in this order: normalcdf (1.4048, 1E99, 0, 1). Your P-value should come out to approximately 0.08. **BUT YOU'RE NOT DONE YET! **Remember, this is a **two-sided z-test**, so you need to **multiply your P-value by 2** to get a final answer of **0.16**.

d.) The problem indicates that the significance level we are supposed to compare our P-value to is 0.05. Therefore, since our P-value is greater than alpha (0.16 > 0.05), **we fail to reject the null hypothesis**.

e.) Now, the final part: state your conclusion in context. At 5% significance, **we do not have enough evidence **to conclude that the mean home price, in thousands of dollars, for this year differs from the mean price in April through June of 2012.