Listed below are several prominent companies and their stock...

Listed below are several prominent companies and their stock prices in June $2004 .$ Go to the Web and look up today's price. There are many sources to find stock prices, such as Yahoo and CNNFI. The Yahoo address is http://www.finance.yahoo.com. Enter the symbol identification to find the current price. At the .05 significance level, can we conclude that the prices have changed?

Key Concepts

Hypothesis Testing

Hypothesis testing is a statistical methodology used to decide whether a claim about a parameter is consistent with a sample of data. It involves formulating a null hypothesis, which represents the status quo or no effect, and an alternative hypothesis, which represents the effect or change being tested. This process allows researchers to use probability theory to assess whether observed data is likely to occur under the null hypothesis.

Null and Alternative Hypotheses

The null hypothesis (H0) is a statement that there is no effect or no difference—in this context, that stock prices have not changed compared to a previous period. The alternative hypothesis (H1) is the counterclaim, stating that stock prices have indeed changed. Establishing these hypotheses clearly frames the statistical test and guides the decision-making process regarding whether to reject the null hypothesis.

Significance Level

The significance level, often denoted by alpha (?), is the threshold used to determine whether an observed effect is strong enough to reject the null hypothesis. In this case, a significance level of 0.05 is used, meaning there is a 5% risk of concluding that there is a change in stock prices when in fact there is none. It is a critical parameter that influences the sensitivity of the hypothesis test.

Paired Sample t-Test

A paired sample t-test is a statistical procedure used to compare two related samples, such as stock prices of the same companies at two different time points. This test is appropriate when the observations are naturally paired, allowing the analysis to focus on the differences within each pair. It helps determine whether the mean difference between paired observations is statistically significantly different from zero, thereby assessing the change over time.

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