The price of a stock of a high tech company has had an average weekly price of $32 for the past several months. Because of recent changes in the company’s management an investor thinks the average weekly price has changed. To test this claim at the 5% level, the investor collects the average weekly price over a period of 15 weeks. The mean for the sample is $33.25. Assume that the distribution of prices is normal with a population standard deviation of $3. In the box below answer the following questions: (a) What is the test statistic? (Round to two decimal places.) (b) What is the p-value? (Round to three decimal places.) (c) What is the conclusion in the context of the problem?

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...