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Stock Market Participation An economist sampled 2200 individuals and found that 983 actively participate in the stock market. a. (2pts) Find the sample proportion. (Round your answer to 4 decimal points) Sample proportion: b. (2pts) True or false, the sample proportion is approximately normally distributed, 0 True 0 False c. (Bpts) Compute a 99% confidence interval for the population proportion p. (Round your answers to 4 decimal points) t0 d. (2pts) Report the margin of error for this confidence level. (Round your answer to 4 decimal points) P-Value Definition (2pts) What is the definition ofa p-value? O The probability that the null hypothesis is incorrect. O A number unrelated to probability that assesses whether or not a scientific claim is true. O The probability of observing a test statistic as in favor of (or more in favor of) the null hypothesis given that the alternative is true. 0 The probability of rejecting the alternative hypothesis given that the null is true. O The probability of observing a test statistic as in favor of (or more in favor of) the alternative hypothesis given that the null is true. 0 The probability of rejecting the null hypothesis given that the alternative hypothesis is true. O The probability that the null hypothesis is correct. Dentists A toothpaste company wants to declare in an ad that more than 80% of dentists recommend their toothpaste. The company performs a hypothesis test at the a = 0.05 significance level to test their claim. The company samples 500 dentists. Of these, 407 recommend their toothpaste. Let ,0 represent the population proportion of dentists that recommend their toothpaste. a. (2pts) Specify the null and alternative hypotheses for the company's claim. 0 H0: p: 0.80; HA: p 0.80 O HO: p: 0.80; HA: pat 0.80 b. (2pts) Calculate the sample proportion. (Round final answer to 4 decimal places) Sample proportion: b. (3pts) Calculate the z or t statistic. (Do not use continuity correction. Round final answer to 4 decimal places) Statistic: c. (2pts) Find the pvalue. {Do not use continuity correction. Round final answer to 4 decimal places) p-value: d. (Zpts) What do you conclude? 0 Do not reject the null hypothesis for the alternative, the results do not support the company's claim. 0 Do not reject the null hypothesis for the alternative, the results support the company's claim. 0 Reject the null hypothesis for the alternative, the results do not support the company's claim. 0 Reject the null hypothesis for the alternative, the results support the company's claim. GDP Based on the average predictions of 40 economists, the U.S. gross domestic product (GDP) will expand by 2.4% this year. Suppose the sample standard deviation of their predictions was 2%. At the 5% significance level, test if the mean forecast GDP of all economists is less than 3%. a. (2pts) Select the null and the alternative hypotheses. O Ho: M = 3; HA: M # 3 O Ho: M = 3; HA: M> 3 O HO: M = 3; HA: M