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 54 stocks traded on the nyse that day showed that 6 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 . what is the test statistic for this sample? (report answer accurate to three decimal places.) test statistic

Answer 1

The test statistic for this sample is -5.55.

How to find test statistic?

The null hypothesis (H₀) is that the proportion of stocks that went up on the NYSE on January 31, 2006, is equal to 0.3. The alternative hypothesis (H₁) is that the proportion of stocks that went up is less than 0.3.

The sample proportion (
`\hat p`) is the proportion of stocks in the sample that went up. In this case,

`\hat p` = 6/54

= 0.111.

The standard error (SE) is a measure of the variability of the sample proportion. It is calculated by the following formula:

`SE = √(\hat p(1 - \hat p) / n)`

where:

`\hat p` = sample proportion

n = sample size

Plugging in the values:

SE = √(0.111(1 - 0.111) / 54) = 0.033

The test statistic (z) is a measure of how far the sample proportion is from the hypothesized proportion. It is calculated by the following formula:

`z = (\hat p - p_0) / SE`

where:

`\hat p` = sample proportion

p₀ = hypothesized proportion (0.3 in this case)

SE = standard error

Plugging in the values:

z = (0.111 - 0.3) / 0.033 = -5.55

Therefore, the test statistic for this sample is -5.55.