Question

2.      Suppose a company wanted to know if there was a significant in the average income of its male and female customers.  Develop a null and alternate hypothesis for such a problem and give a conclusion based on the p-value results of .04.

Assume you are testing at the .05 level of significance.

3.      A company wants to know the useful life of a new revolutionary lightbulb it has just developed.  A mean of 64 of these bulbs revealed a mean useful life of 30,000 with a standard deviation of 1,500 hours.

A.      Use this information to develop a 95% confidence interval for the mean useful life of all new revolutionary lightbulbs.

B.      Use this information to develop a 98% confidence interval for the mean useful life of all new revolutionary lightbulbs.

4.      A pizza delivery company is concerned that it can no longer count on its average variable cost of $ 4.00 or less.  A sample of 36 pizzas revealed a variable cost of $4.05 and a standard deviation of $.25.  Testing at the .05 level of significance.  Develop null and alternate hypothesis for this claim and give a conclusion if your p-value is .06.

Answer 1

1. INCOME OF MALE AND FEMALE

Suppose, random variables X and Y denote income of male and female respectively.

We have to test for null hypothesis

against the alternative hypothesis

We reject our null hypothesis if .

Here, we observe that .

So, we reject our null hypothesis.

Hence, based on the given data we can conclude that there is a significant difference in the average income of male and female customers.

2. LIGHT BULB-

Corresponding statistic is given by

Here,

Degrees of freedom

We know,

   [Using R-code 'qt(1-(1-0.95)/2,63)']

Hence, 95% confidence interval is given by (29625.31, 30374.69).

Again,

   [Using R-code 'qt(1-(1-0.98)/2,63)']

Hence, 98% confidence interval is given by (29552.44, 30447.56).

3. PIZZA DELIVERY COMPANY-

We have to test for null hypothesis

against the alternative hypothesis

We reject our null hypothesis if .

Here, we observe that .

So, we cannot reject our null hypothesis.

Hence, based on the given data we can conclude that there is no significant evidence that it can no longer count on its average variable cost of $ 4.00 or less.

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