BeanZone Coffee is testing a new brand of espresso beans that ...

Question

BeanZone Coffee is testing a new brand of espresso beans that the supplier claims will increase average customer satisfaction, which is currently 7.8 (out of 10). A sample of 35 stores using the new beans reports an average satisfaction score of 8.1 & standard deviation 0.5.

$(B)$ Should BeanZone switch espresso bean suppliers at all stores?

$(A)$ Use $alpha equals 0.10$ to test if the true mean satisfaction score increased.

$H sub 0 colon$ _________ $H_{a} :$ _________

$\overline{x} =$ ________ $n =$ ________ $s =$ ______

Because $P$ -value = _______ [ < | > ] $α =$ _______, we [ REJECT | FAIL TO REJECT ] $H sub 0$ , there is [ ENOUGH | NOT ENOUGH ] evidence to suggest…

Accepted Answer

Welcome to The Practice. In this problem, we have BeanZone Coffee testing a new brand of espresso beans that the supplier claims will increase average customer satisfaction, which is currently 7.8 out of 10. A sample of 35 stores using the new beans reports an average satisfaction score of 8.1 and standard deviation of 0.5. We'd like to use alpha equals point one to test if the true mean satisfaction score increased. Let's begin by writing our hypothesis, where the null hypothesis is going to be that the mean satisfaction score is what we expect it to be, which is 7.8. So our null hypothesis is that mu is equal to 7.8. The alternative hypothesis is what we're trying to test or find evidence for, and in this case, that's whether the true mean satisfaction score increased. So our alternative hypothesis is that maybe mu is greater than 7.8. Next, we should find some key values from the problem. We need x bar, our sample mean, which is 8.1, n, our sample size, which is 35, and s, our sample standard deviation, which is 0.5. And now we're ready to pull out our t I 80 fours and run the test. As a reminder, we can skip step one, which is only for if we've been given data because we've been given statistics. So I'm gonna mark it off and move down to step two, where I'm gonna click on the stat button, scroll two to the right to the test menu, and then choose whether I want to run a z test or a t test. We have not been given the value of sigma, the population standard deviation, which means we'll be doing a t test. So I'm gonna scroll down to it and click enter. That is step two. All set. For step three, we need to enter in the information from the problem. We've been given stats, so we need to navigate over to the stats menu. We can click enter and then just put in our information starting with mu sub zero, which as a reminder is the expected value of the population mean. We can get that from the null hypothesis, and we can see that it is 7.8. So let's put in 7.8. Next, we wanna put in our sample mean of 8.1 and our sample standard deviation of 0.5 and our sample size of 35. Next, we wanna choose the correct alternative hypothesis. We can see that our alternative hypothesis is that mu is greater than 7.8. And because mu sub zero is equal to 7.8, we wanna choose the option greater than mu sub zero. Once that's all set, we can scroll down to calculate and click enter, and that is step three all set, and the results of the test will appear in the viewing window. We can see that our p value is about 5.8 times 10 to the negative fourth, and we want to compare it to our alpha of 0.1. We can see that our p value of 5.8 times 10 to the negative fourth is smaller than our alpha of 0.1, which means that we reject our null hypothesis. So there is enough evidence to suggest that the alternative hypothesis, mu is greater than 7.8, is true. In other words, we have enough evidence to suggest that the true mean satisfaction score increased with the new espresso beans. Great work.

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