Question

The restaurant manager is testing the bartender's ability to pour 45 mL of spirits correctly into a mixed drink. The manager has the bartender pour water into 12 shot glasses to test their ability to pour the correct amount of spirits:

48

45

44

43

46

47

42

46

47

45

47

49

Note: The data appears to be approximately normally distributed.

Test the bartender's ability to pour 45 mL at the 10% level of significance.

b.Calculate the test statistic.t=

Round to three decimal places if necessary

c. Determine the critical value(s) for the hypothesis test.

d. Conclude whether to reject the null hypothesis or not based on the test statistic.

Reject

Fail to Reject

Answer 1

ANSWER:

The null and alternative hypothesis is

Ho :  The bartender's ability to pour 45 mL of spirits correctly into a mixed drink.

H1 : The bartender's ability to pour 45 mL of spirits not correctly into a mixed drink.

Using parameter

b).

We calculate the test statistic using following formula

(Round to three decimal places)

Test statistic = ----------(1)

c).

We determine the critical value(s) for the hypothesis test using t table of critical values

We find critical values using the = 10% level of significance and degrees of freedom = n - 1 = 12 - 1 = 11

Using the alternative hypothesis the above test is two tailed test that is one critical value is negative and other critical value is positive

Critical values of t = 1.796 ----------(2)

d).

We comparing the test statistic with critical values of t and We conclude whether to reject or fail to reject the null hypothesis.

Using the alternative hypothesis the above test is two tailed test

If test statistic lies outside the critical values of t then we reject the null hypothesis otherwise we fail to reject the null hypothesis.

Using equation (1) and (2)

The test statistic = lies within the critical values of t = 1.796

So, we fail to reject the null hypothesis.

That is, The bartender's ability to pour 45 mL of spirits correctly into a mixed drink.

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