Part 1: Practice with the Big Ideas

What proportion of parents feel hopeless when it comes to helping their children with math homework?An educational psychologist claims, based on extensive research, that 56% of parents feel hopeless when it comes to helping their children with math homework.Believing this claimed value is too high, another researcher surveys a random sample of 450 parents and finds that 232 of these parents say they feel hopeless when it comes to helping their children with math homework.If we want to use this information to conduct a hypothesis test, we need to begin with anull hypothesis(i.e., the initial claim being tested) and an alternative hypothesis (i.e., the competing hypothesis that illustrates what we think is really going on).In symbols, these hypotheses are as follows:

H_o:p= 0.56

H_a:p

1) Look carefully at the hypotheses above and answer the following questions about these hypotheses.

A.What does the symbol "p" stand for?

B.Why does the number "0.56" appear in both the null and alternative hypotheses?

C.Why is there a "" (or greater than) sign?

2) Remember that 232 out of a sample of 450 parents said they feel hopeless when it comes to helping their children with math homework.What will the sample proportion (or) be?Please compute this value below andround answer to three decimal places.

3. To be able to conduct a hypothesis test, we will now need to compute a test statistic (using the following formula). Please attempt to compute this test statistic below, showing as much work as you can. p - P Z= p(1 - p) n 4. As part of the process of conducting a hypothesis test, we need to find what's called a probability value, or a p-value for short. This p-value value tells us something about how likely it would be to observe results at least as extreme as what we observed, if the null hypothesis is really true. Based on the test statistic you calculated to answer Question 3, what should the p-value be equal to? Please use Table B to find this p-value. (Hint: Don't forget that since a p-value is a probability, you need to now take the percentile you get from Table B and divide it by 100 to convert it to a probability). 5. We determine if we should reject or fail to reject the null hypothesis based on how the p- value compares to our chosen significance (or alpha) level. If we assume here that we are using a significance level (or an alpha level) of 0.05, should we reject the null hypothesis or fail to reject the null hypothesis? Please explain the reason for your answer. 6. Would the decision you made in response to Question 5 have been different if the significance level had been 0.01 instead of 0.05? Please explain