For Blank 1 . 1O 6 paints Save Answer A local construction company claims that the average cost of building a backyard pool is $32,500. A homeowner, being skeptical about the validity of this claim, asked 25 random pool owners how much their pool cost, and found the average cost was $36,000. On the basis of advice from a local real estate agent, it could be assumed that the standard deviation of pool cost is $7,900. 1. State the direction of the alternative hypothesis used to test the company's claim. Type the letters gt (greater than), ge (greater than or equal to), It (less than), le (less than or equal to) or ne (not equal to) as appropriate in the box. 2. Use the tables in the text to determine the critical value used to conduct the test, assuming a 10% level of significance. If there are two critical values, state only the positive value. 3. Calculate the test statistic, reporting your answer to three decimal places. 4. Is the null hypothesis rejected for this test? Type yes or no. 5. lfthe company's claim is shown later to be true, determine the nature ofthe decision made in the test. Type cd (correct decision), 1 (a Type I error was made) or 2 (a Type II error was made) as appropriate. 6. Regardless of your answer for 4, if the null hypothesis was rejected, could we conclude that the company's claim is valid? Type yes or no