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For the week ended January $15,2009$ , the bullish sentiment of individual investors was27.6$\%($ AAII Journal, February 2009$) .$ The bullish sentiment was reported to be 48.7$\%$ oneweek earlier and 39.7 $\%$ one month earlier. The sentiment measures are based on a poll conducted by the American Assocation of Individual Investors. Assume that each of the bullish sentiment measures was based on a sample size of $240 .$a. Develop a 95$\%$ confidence interval for the difference between the bullish sentiment measures for the most recent two weeks.b. Develop hypotheses so that rejection of the null hypothesis will allow us to conclude that the most recent bullish sentiment is weaker than that of one month ago.c. Conduct a hypotheses test of part (b) using $\alpha=.01 .$ What is your conclusion?

a. $-0.2962$ to $-0.1258$b. $H_{0} : p_{1}=p_{2}, H_{a} : p_{1}<p_{2}$c. There is sufficient evidence to support the claim of that the most recentbullish sentiment is weaker than that of one month ago.

Intro Stats / AP Statistics

Chapter 11

Comparisons Involving Proportions and a Test of Independence

Descriptive Statistics

Confidence Intervals

The Chi-Square Distribution

Cairn University

Oregon State University

Boston College

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in question 55 were given that the proportion of the investor population that has bullish sentiment about the stock market is 39% and were asked to use a recent sample of 450 investors, 41% of whom were bullish, to test the claim that the current proportion of investors that are bullish is significantly greater than the long term proportion of 39%. So right from the question we have some of her information we have the long term proportion is 0.39 and we also have a sample of 450 and the sample proportion is 0.41 So for part, they were asked to state our hypothesis to test the claim that the proportion in the current sample is greater than 39%. So the alternative hypothesis is that proportion is greater than 0.39 and the null hypothesis is that the proportion is less than or equal to you 0.39 and so in part B were as to use the sample to calculate the test statistic and the P value. So our test statistic is, uh, the first thing to note is that end times P is greater than or equal to five and end times. One minus p is also greater than or equal to five. And this tells us that once we satisfy this criteria, our test statistic follows the A normal distribution. Our sample proportions are normally distributed, so our test statistic is therefore it said no in her tested tested comes out the 0.87 Yeah, we should also note that this is an upper tail test because we're testing the claim that proportions air greater than 0.39 So if you go to the standard normal table, the couple value of 0.87 is this value right here? 0.8078 So this is the area to the left of our test statistic, and we want we're interested. R p values the area in the upper tail beyond the test statistics. So it's one minus this value, so we can say that he value is equal to one minus 0.8078 So that answers Part B and then part C is we're told at the significance level of Alfa equals 0.10 What is their conclusions regarding our test? So we can say that the T value is greater than Alva should finish calculating this year. A point 19 to you too is greater than Alfa. Therefore, we failed to reject the know head offices and we can state that we have insufficient evidence to justify the claim that the current population investors, um has a greater proportion than 39% were bullish about the market.

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