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Chapter 9: Q 37. (page 581)

Fair coin? You want to determine if a coin is fair. So you toss it 10times and record the proportion of tosses that land 鈥渉eads.鈥� You would like to perform a test of H0:p=0.5versus Ha:p鈮�0.5, where p= the proportion of all tosses of the

coin that would land 鈥渉eads.鈥� Check if the conditions for performing the significance test are met.

Short Answer

Expert verified

No, all the conditions are not satisfied.

Step by step solution

01

Given Information

It is given that n=10

p=0.50

The null and alternate hypothesis are:

H0:p=0.50

Ha:p鈮�0.50

pare the proportion of coins that land head.

02

Calculations

The conditions to fulfilled for significance test are:

  • n脳p鈮�10: role="math" localid="1654610961025" n脳p=10脳0.5=5<10
  • n脳(1-p)鈮�10: n脳(1-p)=10脳(1-0.5)=5<10

Both conditions are not fulfilled. Hence, significance test cannot be performed.

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Most popular questions from this chapter

The standardized test statistic for a test of H0:p=0.4versus Ha:pnotequalto0.4isz=2.43This test is

a. not significant at either 伪=0.05or 伪=0.01

b. significant at 伪=0.05but not at伪=0.01

c. significant at伪=0.01but not at 伪=0.05

d. significant at both 伪=0.05and伪=0.01

e. inconclusive because we don鈥檛 know the value of p^

Based on the P-value in Exercise 31, which of the following would be the most

appropriate conclusion?

a. Because the P-value is large, we reject H0. We have convincing evidence that more than 50%of city residents support the tax increase.

b. Because the P-value is large, we fail to reject H0. We have convincing evidence that more than 50%of city residents support the tax increase.

c. Because the P-value is large, we reject H0. We have convincing evidence that at most 50%of city residents support the tax increase.

d. Because the P-value is large, we fail to reject H0. We have convincing evidence that at most 50%of city residents support the tax increase.

e. Because the P-value is large, we fail to reject H0. We do not have convincing

evidence that more than 50%of city residents support the tax increase.

Teen drivers Refer to Exercise 51.

a. Construct and interpret a 95% confidence interval for the true proportion p of all teens in the state who passed their driving test on the first attempt. Assume that the conditions for inference are met.

b. Explain why the interval in part (a) provides more information than the test in Exercise 51.

Bags of a certain brand of tortilla chips claim to have a net weight of 14ounces. Net weights vary slightly from bag to bag and are Normally distributed with mean 渭 . A representative of a consumer advocacy group wishes to see if there is convincing evidence that the mean net weight is less than advertised and so intends to test the hypotheses

H0:渭=14Ha:渭<14

A Type I error in this situation would mean concluding that the bags

a. are being underfilled when they aren鈥檛.

b. are being underfilled when they are.

c. are not being underfilled when they are.

d. are not being underfilled when they aren鈥檛.

e. are being overfilled when they are underfilled

1 A software company is trying to decide whether to produce an upgrade of one of its programs. Customers would have to pay \(100 for the upgrade. For the upgrade to be profitable, the company must sell it to more than 20% of their customers. You contact a random sample of 60 customers and find that 16 would be willing to pay \)100 for the upgrade.

a. Do the sample data give convincing evidence that more than 20% of the company鈥檚 customers are willing to purchase the upgrade? Carry out an appropriate test at the 伪=0.05significance level.

b. Which would be a more serious mistake in this setting鈥攁 Type I error or a Type II error? Justify your answer.

c. Suppose that 30% of the company鈥檚 customers would be willing to pay $100 for the upgrade. The power of the test to detect this fact is0.60. Interpret this value.
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