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Chapter 9: Q. 76. (page 607)

How much juice? One company鈥檚 bottles of grapefruit juice are filled by a machine that is set to dispense an average of 180 milliliters (ml) of liquid. The company has been getting negative feedback from customers about underfilled bottles. To investigate, a quality-control inspector takes a random sample of 40 bottles and measures the volume of liquid in each bottle. The mean amount of liquid in the bottles is 179.6 ml and the standard deviation is 1.3 ml. Do these data provide convincing evidence at the伪=0.05significance level that the machine is underfilling the bottles?

Short Answer

Expert verified

The required answer is:

Yes, there is sufficient evidence to show that bottles are being unfilled by the machine.

Step by step solution

01

Given information

Population mean (渭)=180

Sample mean (x炉)=179.6

Sample size (n)=40

Sample standard deviation(s)=1.3

02

Formula used

We know,

The test statistic formula is:t=x炉-渭osn

03

Calculation

The null and alternative hypotheses are as follows:

H0:渭=180Ha:渭<180

The alternative hypothesis denotes that the test is left-handed.

The Minitab output is as follows:

The p-value is 0.029

Here, p-value (0.029)<伪(0.05)The null hypothesis is rejected.

There is enough evidence to show that the machine is unfilling bottles at the 5%level of significance.

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Most popular questions from this chapter

Pressing pills Refer to Exercise 77.

a. Construct and interpret a 95% confidence interval for the true hardness 渭 of the tablets in this batch. Assume that the conditions for inference are met.

b. Explain why the interval in part (a) is consistent with the result of the test in Exercise 77.

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Philly fanatics? Nationally, the proportion of red cars on the road is 0.12.A statistically minded fan of the Philadelphia Phillies (whose team color is red) wonders if Phillies fans are more likely to drive red cars. One day during a home game, he takes a random sample of 210cars parked at Citizens Bank Park (the Phillies home field), and counts 35red cars.

a. State appropriate hypotheses for performing a significance test. Be sure to define the parameter of interest.

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