The marketing manager of a firm that produces laundry products decides to test market a new laundry product in each of the firm's two sales regions. He wants to determine whether there will be a difference in mean sales per market per month between the two regions. A random sample of 13 supermarkets from Region 1 had mean sales of 80.9 with a standard deviation of 7.8. A random sample of 17 supermarkets from Region 2 had a mean sales of 72.7 with a standard deviation of 6. Does the test marketing reveal a difference in potential mean sales per market in Region 2? Let u, be the mean sales per market in Region 1 and u2 be the mean sales per market in Region 2. Use a significance level of a = 0.02 for the test. Assume that the population variances are not equal and that the two populations are normally distributed. Step 1. State the null and alternative hypotheses for the test. Answer: Step 2. Compute the value of the t test statistic. Round your answer to three decimal places. Answer: Step 3. Determine the decision rule for rejecting the null hypothesis Ho. Round your answer to three decimal places. Answer: Step 4. State the test's conclusion. A) Reject Null Hypothesis B) Fail to Reject Null Hypothesis

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Compound Probability

Compound probability can be defined as the probability of the two events which are independent. It can be defined as the multiplication of the probability of two events that are not dependent. 

Tree diagram

Probability theory is a branch of mathematics that deals with the subject of probability. Although there are many different concepts of probability, probability theory expresses the definition mathematically through a series of axioms. Usually, these axioms express probability in terms of a probability space, which assigns a measure with values ranging from 0 to 1 to a set of outcomes known as the sample space. An event is a subset of these outcomes that is described. 

Conditional Probability

By definition, the term probability is expressed as a part of mathematics where the chance of an event that may either occur or not is evaluated and expressed in numerical terms. The range of the value within which probability can be expressed is between 0 and 1. The higher the chance of an event occurring, the closer is its value to be 1. If the probability of an event is 1, it means that the event will happen under all considered circumstances. Similarly, if the probability is exactly 0, then no matter the situation, the event will never occur.