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 62 stocks traded on the NYSE that day showed that 27 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=0.10α=0.10.

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

Given,

1)

2) sample size i.e

3)

4)

As given in the problem A sample of 62 stocks traded on the NYSE that day showed that 27 went up.

so we can calculate sample proportion as,

Here,

State the hypothesis,

• Step1:- Test statistics

Here we are using one-tailed  Z test,

test statistics up to three decimal point

• Step2:- Calculating P-value

The p-value can be found from Standard Normal Table

P-value will found from our Alternative hypothesis

Here,

For

We find the probability value for

Using Standard Normal Table

Using Interpolation we can find the value for   

• Interpolation Formula

Using this formula,

Therefore,

Here

The p-value is less than

• Step3:- Decision

This test statistic leads to a decision to,

Since 0.0812588 is less than 0.1 we will reject the null hypothesis i.e

• Step4:-Conclusion

As such, the final conclusion is that,

The sample data support the claim that the proportion of stocks that went up is more than 0.3.