The price of a stock of a high tech company has had an average weekly price of $36 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 17 weeks. The mean for the sample is $37.5. Assume that the distribution of prices is normal with a population standard deviation of $3. (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?
Continuous Probability Distributions
Probability distributions are of two types, which are continuous probability distributions and discrete probability distributions. A continuous probability distribution contains an infinite number of values. For example, if time is infinite: you could count from 0 to a trillion seconds, billion seconds, so on indefinitely. A discrete probability distribution consists of only a countable set of possible values.
Normal Distribution
Suppose we had to design a bathroom weighing scale, how would we decide what should be the range of the weighing machine? Would we take the highest recorded human weight in history and use that as the upper limit for our weighing scale? This may not be a great idea as the sensitivity of the scale would get reduced if the range is too large. At the same time, if we keep the upper limit too low, it may not be usable for a large percentage of the population!
The price of a stock of a high tech company has had an average weekly price of $36 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 17 weeks. The mean for the sample is $37.5. Assume that the distribution of prices is normal with a population standard deviation of $3.
(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?
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