Apolling organization reported data from a survey of 2000 randomly selected canadians who carry debit cards. participants in this survey were asked what they considered the minimum purchase amount for which it would be acceptable to use a debit card. suppose that the sample mean and standard deviation were $9.11 and $7.30, respectively. (these values are consistent with a histogram of the sample data that appears in the report.) do these data provide convincing evidence that the mean minimum purchase amount for which canadians consider the use of a debit card to be appropriate is less than $10? carry out a hypothesis test with a significance level of 0.01. (use a statistical computer package to calculate the p-value. round your test statistic to two decimal places and your p-value to three decimal places.) t = ? p-value = ?

Null hypothesis:    

Alternative hypothesis :  

And we can use the following excel code: "=T.DIST(-5.45,1999,TRUE)"

Step-by-step explanation:

Data given and notation  

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.  

t would represent the statistic (variable of interest)  

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

State the null and alternative hypotheses.  

Is a one tailed left test.  

What are H0 and Ha for this study?  

Null hypothesis:    

Alternative hypothesis :  

Find the rejection region for the test using significance level=.01

First we need to find the degrees of freedom on this case:

In order to find the critical value we need to find a value on the t distirbution such that:  

where 0.01 represent the significance level selected.  

And this value is  

We can use the following excel code: "=T.INV(0.01,1999)"

The rejection regin would be (-infinity;-2.33)

Compute the test statistic

The statistic for this case 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".  

Calculate the statistic  

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

Give the appropriate conclusion for the test

Since is a one side left tailed test the p value would be:  

And we can use the following excel code: "=T.DIST(-5.45,1999,TRUE)"

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.

R code

1. sometimes

2.   never

3   .08c = 7.50+.05c   250 pages

step-by-step explanation:

1.   sometimes

the theoretical probability of rolling a 1 is 1/6.   perhaps you got really lucky and never rolled a 1   in those 60 times.   your experimental probability is 0.   or perhaps you rolled a 1   20 times.   your experimental probability is 20/60 is 1/3.     it really just depends on how you rolled in that experiment.

2.   never

the probability of the event occurring is 1.   that is being 100 % sure it will happen.   that is the maximum amount of confidence we have.

3.   no customer card cost:   .08 times number of pages

customer card cost:   7.50 + .05 times number of pages

we want to find when it costs the same amount, so we will set these equal

let c = number of pages

.08c = 7.50+.05c

subtract .05c from each side

.08c-.05c = 7.5+.05c-.05c

.03c=7.5

divide each side by .03

.03c/.03 = 7.5/03

c =250  

the cost is the same at 250 pages

you just switch the numbers basically so it would be 3/17