Question

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 65 stocks traded on the NYSE that day showed that 15 went up. You are conducting a study to see if the proportion of stocks that went up is is significantly less than 0.3. You use a significance level of α = 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 = Incorrect

Answer 1

Solution :

This is the left tailed test .

The null and alternative hypothesis is

H₀ : p = 0.3

H_a : p < 0.3

= x / n = 15 / 65 = 0.2308

P₀ = 0.3

1 - P₀ = 0.7

Test statistic = z

= - P₀ / [P_{0 *} (1 - P₀ ) / n]

= 0.2308 - 0.3/ [(0.3 * 0.7) / 65]

= -1.218

Test statistic = z = -1.218

P(z < -1.218) = 0.1116

P-value = 0.1116

= 0.05

P-value <

Reject the null hypothesis .

There is sufficient evidence to suggest that