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Chapter 9: Q 89. (page 609)

Potato power problems Refer to Exercises 85 and 87

a. Explain one disadvantage of using 伪=0.10 instead of 伪=0.05 when

performing the test.

b. Explain one disadvantage of taking a random sample of 500 potatoes instead of 250 potatoes from the shipment.

Short Answer

Expert verified

Part (a) There is the most likely to have a type I error

Part (b) More time-consuming and costly to collect the data.

Step by step solution

01

Part (a) Step 1: Given information

H0:p=0.08Ha:p>0.08,p=0.11,n=500伪=0.05
02

Part (a) Step 2: Explanation

Type I error: Reject the null hypothesis H0, once the null hypothesis H0

is true.

伪Showing the probability of a type I error.

If you increase 伪=0.05to伪=0.10 the likelihood of making a type I error increases, and you're more likely to make one, which is a negative.

03

Part (b) Step 1: Explanation

If the sample size is increased from 250 to 500 potatoes, data collection will be more time-consuming and costly for the 500 potatoes than for the 250 potatoes (as there are twice as many potatoes about which we need to collect data).

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Most popular questions from this chapter

Making conclusions A student performs a test of H0:p=0.75versus Ha:p<0.75at 伪=0.05significance level and gets a P-value of 0.22

The student writes: 鈥淏ecause the P-value is large, we accept H0. The data provide convincing evidence that null hypothesis is true". Explain what is wrong with this conclusion.

Significance tests A test of H0:p=0.65 against Ha:p<0.65

based on a sample of size 400 yields the standardized test statistic z=鈭�1.78 .

a. Find and interpret the P-value.

b. What conclusion would you make at the 伪=0.10 significance level? Would

your conclusion change if you used 伪=0.05 instead? Explain your reasoning.

c. Determine the value of p铃�= the sample proportion of successes.

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?

Interpreting a P-value A student performs a test of H0:渭=100H0:渭=100versus Ha: 渭>100Ha:渭>100and gets a P-value of 0.044.The student says, "There is a0.044 probability of getting the sample result I did by chance alone." Explain why the student's explanation is wrong.

Losing weight A Gallup poll found that 59% of the people in its sample said 鈥淵es鈥� when asked, 鈥淲ould you like to lose weight?鈥� Gallup announced: 鈥淔or results based on the total sample of national adults, one can say with 95% confidence that the margin of (sampling) error is 卤3 卤3percentage points.鈥�12 Based on the confidence interval, is there convincing evidence that the true proportion of U.S. adults who would say they want to lose weight differs from 0.55? Explain your reasoning
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