Question

QUESTION PART A : If n = 300 and ˆp(p-hat) = 0.3, construct a 90% confidence interval.

Give your answers to three decimals

< p <

QUESTION PART B: You want to obtain a sample to estimate a population proportion. At this point in time, you have no reasonable estimate for the population proportion. You would like to be 99.9% confident that you esimate is within 1.5% of the true population proportion. How large of a sample size is required?

PART C: 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 74 stocks traded on the NYSE that day showed that 26 went up.

You are conducting a study to see if the proportion of stocks that went up is is significantly more than 0.3. You use a significance level of α=0.005α=0.005.

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...

• less than (or equal to) αα
• greater than αα

This test statistic leads to a decision to...

• reject the null
• accept the null
• 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 is more than 0.3.
• There is not sufficient evidence to warrant rejection of the claim that the proportion of stocks that went up is is more than 0.3.
• The sample data support the claim that the proportion of stocks that went up is is more than 0.3.
• There is not sufficient sample evidence to support the claim that the proportion of stocks that went up is is more than 0.3.

Answer 1

This test statistic leads to a decision to...fail to reject the null.
As such, the final conclusion is that...There is not sufficient sample evidence to support the claim that the proportion of stocks that went up is is more than 0.3.