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A recent article concerning bullish and bearish sentiment about the stock market reported that 41$\%$ of investors responding to an American Institute of Individual Investors (AAII) poll were bullish on the market and 26$\%$ were bearish $(U S A$ Today, January $11,2010) .$ The article also reported that the long-term average measure of bullishness is 39 or 39$\% .$ Suppose the AAIl poll used a sample size of $450 .$ Using. 39 (the long-term average) as the population proportion of investors that are bullish, conduct a hypothesis test to determine if the current proportion of investors that are bullish is significantly greater than the long-term average proportion.a. State the appropriate hypotheses for your significance test.b. Use the sample results to compute the test statistic and the $p$ -value.c. Using $\alpha=.10,$ what is your conclusion?

a. $H_{0} : p \leq 39 \%=0.39, H_{a} : p>0.39$b. $z=0.87, P=0.1922$c. There is not sufficient evidence to support the claim that the currentproportion of investors that are bullish is significantly greater than thelong-term proportion.

Intro Stats / AP Statistics

Chapter 9

Hypothesis Tests

Confidence Intervals

Hypothesis Testing with One Sample

Hypothesis Testing with Two Samples

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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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