According to the Coffee Research Organization the typical American coffee drinke

Question

According to the Coffee Research Organization the typical American coffee drinker consumes an average of 3.1 cups per day, with a population standard deviation of 0.58 cups. After a new coffee campaign is launched by the coffee industry, marketers believe the amount of coffee consumed is now greater than 3.1 cups per day. State the null hypothesis and the alternative hypothesis. The level of significance is 0.05. Select the test statistic. Formulate the decision rule. Make a decision. Interpret the result. Are the marketers right?

Explanation / Answer

Given:

.

Steps to conduct the hypothesis test are as follows:

Step I : Framing the Hypothesis:

Null hypothesis: Population mean is 3.1 cups per day

Ho: µ = 3.1

Alternate Hypothesis: Population mean is greater than 3.1 cupes per day

Ha: µ > 3.1 ....................[right tailed test]

.

Step II: Set the sginificance level

The significance level() to test the hypothsis is mentioned in the question as 0.05

.

Step III: Calculate Test statistic:

Z = (X - µ)/

Since we want X> 3.1

Hence Z > (3.1-3.1)/0.58

Z > 0

The test statistic should be greater than 0 , in order to get the coffee consumption above 3.1 cups a day

.

Step IV: Calculate Critical value of Z for = 0.05, right tailed Z test

Zcritical = 1.645 , for =0.05 one tailed Z test

.

Step V: Decision rule:

.

Decision: Since we have Z statistic = 0 , which is less that Z critical =1.645 , hence we fail to reject the null hypothesis

.

Step VI: Interpretation of result:

Since Z statistic is less than the Z critical value, we fail to reject the nul hypothesis and thu agree that the population mean is 3.1 cups per day , and not greater than this.

Hence the marketers are NOT right

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