Question

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Google became a publicly-traded company in August 2004. Initially, the stock traded over 10 million shares each day! Since the initial offering, the volume of stock traded daily has decreased substantially. In 2010, the mean daily volume in Google stock was 5.44 million shares, according to Yahoo! Finance. A random sample of 35 trading days in 2014 resulted in a sample mean of 3.28 million shares with a standard deviation of 1.68 million shares. Does the evidence suggest that the volume of Google stock has changed since 2007? Use a 0.05 level of significance.

1. State the null and alternative hypotheses.
2. What type of hypothesis test is to be used?
3. What distribution should be used and why?
4. Is this a right, left, or two-tailed test?
5. Compute the test statistic.
6. Compute the p-value.
7. Do you reject or not reject the null hypothesis? Explain why.
8. What do you conclude?

Answer 1

Solution:-

1)

State the hypotheses. The first step is to state the null hypothesis and an alternative hypothesis.

Null hypothesis: u = 5.44
Alternative hypothesis: u 5.44

2)

The test method is a one-sample t-test

3)

T distribution must be used.

4)

This is a two tailed test

For this analysis, the significance level is 0.05. We should use student's t-distribution, because population standard deviation is unknown and sample size is large enough(n > 30).

5)

Analyze sample data. Using sample data, we compute the standard error (SE), degrees of freedom (DF), and the t statistic test statistic (t).

SE = s / sqrt(n)

= 1.68/sqrt(35)

S.E = 0.28397

DF = n - 1

D.F = 34
test statistic = (x - u) / SE

= (5.44-3.28)/0.28397

t = 7.61

where s is the standard deviation of the sample, x is the sample mean, u is the hypothesized population mean, and n is the sample size.

Since we have a two-tailed test, the P-value is the probability that the t statistic having 34 degrees of freedom is less than -7.61 or greater than 7.61.

6)

P(Z=7.61)

Thus, the P-value = 0 (From Z table)

Interpret results.

7)

Since the P-value (almost 0) is less than the significance level (0.05), we have to reject the null hypothesis.

8)

From the above test we have sufficient evidence in the favor of the claim that the volume of google stock has changed since 2007.