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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

Watching grass grow The germination rate of seeds is defined as the proportion of seeds that sprout and grow when properly planted and watered. A certain variety of grass seed usually has a germination rate of 0.80. A company wants to see if spraying the seeds with a chemical that is known to increase germination rates in other species will increase the germination rate of this variety of grass. The company researchers spray a random sample of 400grass seeds with the chemical, and 339of the seeds germinate. Do these data provide convincing evidence at the 伪=0.05 significance level that the chemical is

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of all teens pass their driving test on the first attempt. An investigative reporter examines an SRS of the DMV records for 125teens; 86of them passed the test on their first try. Is there convincing evidence at the 伪=0.05significance level that the DMV鈥檚 claim is incorrect?

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Tests and confidence intervals The P-value for a two-sided test of the null hypothesis H0:渭=15is0.03

a. Does the 99% confidence interval for 渭 include 15? Why or why not?

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Walking to school Refer to Exercise 36.

a. Explain why the sample result gives some evidence for the alternative hypothesis.

b. Calculate the standardized test statistic and P-value.

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