- Many Investors And Financial Analysts Believe The Dow Jones Industrial Average Djia Gives A Good Barometer Of The Over 1 (241.08 KiB) Viewed 83 times
Many investors and financial analysts believe the Dow Jones Industrial Average (DJIA) gives a good barometer of the overall stock market. On January 31, 2006, 9 of the 30 stocks making up the DJIA increased in price (The Wall Street Journal, February 1, 2006). On the basis of this fact, a financial analyst claims we can assume that 30% of the stocks traded on the New York Stock Exchange (NYSE) went up the same day. A sample of 78 stocks traded on the NYSE that day showed that 12 went up. You are conducting a study to see if the proportion of stocks that went up is significantly less than 0.3. You use a significance level of a = 0.05. What is the test statistic for this sample? (Report answer accurate to three decimal places.) test statistic = What is the p-value for this sample? (Report answer accurate to four decimal places.) p-value = The p-value is... O less than (or equal to) a Ogreater than a This test statistic leads to a decision to... O reject the null O accept the null O fail to reject the null As such, the final conclusion is that... There is sufficient evidence to warrant rejection of the claim that the proportion of stocks that went up is less than 0.3. There is not sufficient evidence to warrant rejection of the claim that the proportion of stocks that went up is less than 0.3. The sample data support the claim that the proportion of stocks that went up is less than 0.3. There is not sufficient sample evidence to support the claim that the proportion of stocks that went up is less than 0.3.
You wish to test the following claim (Ha) at a significance level of a = 0.002. Ho:p = 0.68 Ha:p > 0.68 You obtain a sample of size n = 726 in which there are 511 successful observations. For this test, you should NOT use the continuity correction, and you should use the normal distribution as an approximation for the binomial distribution. What is the test statistic for this sample? (Report answer accurate to three decimal places.) test statistic = What is the p-value for this sample? (Report answer accurate to four decimal places.) p-value = The p-value is... O less than (or equal to) a O greater than a This test statistic leads to a decision to... O reject the null O accept the null O fail to reject the null As such, the final conclusion is that... There is sufficient evidence to warrant rejection of the claim that the population proportion is greater than 0.68. There is not sufficient evidence to warrant rejection of the claim that the population proportion is greater than 0.68. The sample data support the claim that the population proportion is greater than 0.68. There is not sufficient sample evidence to support the claim that the population proportion is greater than 0.68.
5.7 Sleep habits of New Yorkers: New York is known as "the city that never sleeps". A random sample of 25 New Yorkers were asked how much sleep they get per night. Statistical summaries of these data are shown below. Do these data provide strong evidence that New Yorkers sleep less than 8 hours a night on average? n X min max 25 7.73 0.77 6.17 9.78 S (a) Write the hypotheses in symbols. OHo: H = 8 Ha: = 8 O Ho: 4 = 8 Ha: > 8 OHo: 4 = 8 Ha: 4 < 8 (b) Calculate the test statistic, T, and the degrees of freedom. T = (please round to two decimal places) There are degrees of freedom associated with this test. (c) Find and interpret the p-value in this context. Drawing a picture may be helpful. p = (please round to four decimal places) (d) What is the conclusion of the hypothesis test? Since p<a we reject the null hypothesis and accept the alternative O Since p 2 a we do not have enough evidence to reject the null hypothesis Since p 2 a we accept the null hypothesis Since p<a we fail to reject the null hypothesis O Since p 2 a we reject the null hypothesis and accept the alternative