Question

The Federal Reserve Board of Governors recently changed the reporting of its stance on monetary policy from what they termed a "policy bias" to a "balance of risks". A researcher wished to see whether there had been a change in the way financial analysts were interpreting the change in reporting. When the "policy bias" reporting method was used, it was known that only 35% of the Board's decisions were correctly anticipated by analysts in their reports. For the "balance of risks" method, the researcher took a random sample of 56 analysts' reports and found that 26 of these correctly anticipated the Board's decision. Assume that the test is to be carried out at the 10% level.

1. State the direction of the alternative hypothesis used to test whether the proportion of analysts correctly anticipating the Board's decision had changed. 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 in the box.
2. Calculate the test statistic, reporting your answer to two decimal places.
3. Use the tables in the textbook to determine the p-value for the test (answer to 4 decimal places)
4. Is the null hypothesis rejected for this test? Type yes or no.
5. Disregarding your answer for 4, if the null hypothesis was rejected at the 10% level, would the predictive accuracy of the claims in analysts' reports appear to have changed under the new system? Type yes or no.

Answer 1

1. Here claim is that p is different from 0.35

Here claim is that p is different from 0.35 H_0: p = 0.35 vs H_1: p notequalto 0.35 As n > 30, we will use z statistics p^= 26/56 = 0.46 SEP = squareroot pq/n = squareroot 0.35 * 0.65/56 = 0.0637 Hence z = p^- p/SEP = 0.46 - 0.35/0.0637 = 1.73 P value is 2P(z > 1.73) = 2 * 0.0418 = 0.0836 As P value is less than alpha = 0.10, we reject the null hypothesis Yes.
vs

2. As n>30, we will use z statistics

Hence

3. P value is

4. As P value is less than alpha=0.10, we reject the null hypothesis

Yes.