Final answer:
To perform a hypothesis test for the stock price growth rate, the null hypothesis states the stock grows at $5 per week, and the alternative that it grows at a different rate. After calculating a test statistic and determining the p-value, one can conclude whether to reject the null hypothesis based on the significance level. Type I and Type II errors represent possible mistakes in this testing.
Step-by-step explanation:
The original statement about the price of stock A increasing is related to mathematics, specifically to the concept of growth rates in finance. However, the question then leads into a hypothesis test regarding the growth rate of a particular stock, which is definitely a statistical concept generally covered in college-level mathematics or business courses.
The student is asked to perform a hypothesis test using historical stock price data and a given expected growth rate. Here, we lay out the steps for hypothesis testing:
- State the null hypothesis (H0): The stock grows at the rate of $5 per week.
- State the alternative hypothesis (H1): The stock grows at a rate different than $5 per week.
- Collect the sample data and calculate the sample mean.
- Use the sample data to calculate the test statistic, which in this case could be a t-statistic since we have the standard deviation and not the variance.
- Determine the p-value associated with the observed test statistic.
- Compare the p-value to the significance level (0.05) to decide whether to reject H0.
The conclusion is based on whether the p-value is lower than the significance level. A p-value lower than 0.05 would lead to rejecting the null hypothesis, indicating that the stock does not grow at $5 per week.
Type I error is rejecting H0 when it is true (false positive), and Type II error is failing to reject H0 when it is false (false negative).