A member of the Islip Urban Renewal Taskforce claimed, after the installation of internal heating facilities in homes, the proportion of homes with...

A member of the Islip Urban Renewal Taskforce claimed, after the installation of internal heating facilities in homes, the proportion of homes with fireplaces fell below 50%. 

1. State the direction of the alternative hypothesis used to test the taskforce claim. Type gt (greater than), ge (greater than or equal to), lt (less than), le (less than or equal to) or ne (not equal to) as appropriate on the right.

Another committee member, who did not originally believe the claim, took a random sample of 84 houses in the area to test the validity of the claim. He found that 35 of them had fireplaces.

2. Use the tables in the textbook to determine the critical value of the test statistic using a 4% level of significance. If there are two critical values, state only the positive value. 

3. Calculate the test statistic, correct to two decimal places. 

4. Is the null hypothesis rejected for this test? Type yes or no. 

5. Regardless of your answer for 4, if the null hypothesis was not rejected, can we conclude after the installation of internal heating facilities in homes, the proportion of homes with fireplaces fell below 50% at the 4% level of significance? Type yes or no.