Question

Do you have bad breath? A machine is programmed to fill bottles with 1.65 liters of mouthwash in each bottle. Scope is testing that machine for its accuracy. In a sample of 29 bottles of mouthwash, the mean and standard deviation are calculated as 1.77 liters and 0.25 liters, respectively. Use Table 2.

a.	Select the null and the alternative hypotheses to determine if the machine is working improperly, that is, it is either underfilling or overfilling the bottles of mouthwash.
	H0: µ ? 1.65; HA: µ < 1.65 H0: µ ? 1.65; HA: µ > 1.65 H0: µ = 1.65; HA: µ ? 1.65

b.	Calculate the value of the test statistic. (Round your answer to 2 decimal places.)

Test statistic

c.	Approximate the p-value.
	0.01< p-value < 0.02 0.02 < p-value < 0.05 0.05 < p-value < 0.10

d.	What is the conclusion at the 1% significance level?
	Reject H0 since the p-value is greater than ?. Reject H0 since the p-value is smaller than ?. Do not reject H0 since the p-value is greater than ?. Do not reject H0 since the p-value is smaller than ?.

e.	Calculate the critical value(s) at a 1% level of significance. (Round your answer to 3 decimal places.)

Critical value(s)

±

f.	Can you conclude that the machine is working improperly?
	Yes No

Answer 1

(A) we have to test whether the machine is filling less or more liters of mouthwash in each bottles, so it clearly a two tailed hypothesis

Null hypothesis:-

Alternate hypothesis:

so, option C is correct and other two options are showing hypotheses for one tailed test, thats why those two options are incorrect.

We are using t statistic because the population standard deviation in unknown and the sample size is also less than 29

(B) we have

Using the t statistisc formula, we can write

t statistic =

setting the values, we get

t statistic =

(C)

Using student's t distribution table for the t value of 2.58 for 0.01 significance level and degree of freedom = n-1 = 29-1 = 28, we get the p value

p value= 0.0154

So, p value is between 0.01 and 0.02

option A is correct

(D) Since the p value of 0.0154 is greater than 0.01, i.e. the p value is insignificant at 1% significance level, so we fail to reject the null hypothesis and we can conclude that the machine is not accurate at 0.01 significance level.

so, option A (Reject H0 since the p-value is greater than ?.) is correct

(E) Critical value using the t distribution for 1% level of significance with degree of freedom = n-1 = 29-1 = 28

we get

t critical =

((F) YES because we fail to reject the null hypothesis, which means the alternate hypothesis is false and we can say that the machine is working improperly.