Fowle Marketing Research Inc., bases charges to a client on the assumption that telephone surveys can be completed in a mean time of 15 minutes or less. If a longer mean survey time is necessary, a premium rate is charged. A sample of 35 surveys provided the following survey times in minutes: 17;11;12;23;20;23;15;16;23;22;18;23 ;25;14;12;12;20;18;12;19;11;11;20;2 1;11;18;14;13;13;19; 16;10;22;18;23. Based upon past studies, the population standard deviation is assumed known with s = 4 minutes. Is the premium rate justified?

a. Formulate the null and alternative hypotheses for this application.
b. Compute the value of the test statistic.
c. What is the p-value?
d. At a = .01, what is your conclusion?

a) Null hypothesis:  

Alternative hypothesis:  

b)      

c)    

d) If we compare the p value and the significance level given we see that so we can conclude that we have enough evidence to reject the null hypothesis, so we can conclude that the true mean is higher than 15 at 1% of signficance.  

Step-by-step explanation:

Data given and notation  

The sample mean is given by:

And the sample deviation is:

represent the sample mean    

represent the sample standard deviation

sample size  

represent the value that we want to test  

represent the significance level for the hypothesis test.  

z would represent the statistic (variable of interest)  

represent the p value for the test (variable of interest)  

Part a State the null and alternative hypotheses.  

We need to conduct a hypothesis in order to check if the mean is less or equal than 15, the system of hypothesis would be:  

Null hypothesis:  

Alternative hypothesis:  

Since we don't  know the population deviation, is better apply a t test to compare the actual mean to the reference value, and the statistic is given by:  

(1)  

t-test: "Is used to compare group means. Is one of the most common tests and is used to determine if the mean is (higher, less or not equal) to an specified value".  

Part b Calculate the statistic  

We can replace in formula (1) the info given like this:  

Part c P-value  

The degrees of freedom are given by:

Since is a right tailed test the p value would be:  

Part d Conclusion  

If we compare the p value and the significance level given we see that so we can conclude that we have enough evidence to reject the null hypothesis, so we can conclude that the true mean is higher than 15 at 1% of signficance.  

saving = more money

step-by-step explanation:

if you have 100 bucks, and you want to buy a candy bar, even if you have one at home, if you choose not to buy it, you save.

~courtney

the ratio of grapes to blueberries she should use is 12: 3

step-by-step explanation:

if mandie is making 15 cups of fruit salad, the ratio of grapes to blueberries she should use is 12: 3.