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Chapter 9: Q.76 (page 543)

The cost of a daily newspaper varies from city to city. However, the variation among prices remains steady with a

standard deviation of 20垄. A study was done to test the claim that the mean cost of a daily newspaper is $1.00. Twelve costs

yield a mean cost of 95垄 with a standard deviation of 18垄. Do the data support the claim at the 1% level?

Short Answer

Expert verified

The data support the claim that the mean cost of a daily news paper is $1.00

Step by step solution

01

Given Information

Given

the sample size n=12

Twelve costs yield a mean cost of $0.95with a standard deviation of $0.18

mean of the samplelocalid="1650204298826" (x鈦�)=$0.95

Standard deviation of sample (S)=$0.18

Given claim that the mean cost of a daily newspaper is $1.00.

The mean of the population '渭'=$1.00.

Null hypothesis:-H鈧赌:'渭'=$1.00.

Alternative hypothesis:H鈧�:'渭'鈮�$1.00.

level of significance鈭�=0.01

02

Explanation

The test statistic on calculation, we get

t=-0.96

|t|=|-0.96|=0.96

Degrees of freedom纬=n-1=12-1=11

t鈧�=2.718

Calculated value t=0.96

Tabulated value t=0.01level for 11掳for two tailed test = 2.718

since calculated' t' value is less than tabulated value 't'.

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Most popular questions from this chapter

Marketers believe that 92%of adults in the United States own a cell phone. A cell phone manufacturer believes that number is actually lower. 200American adults are surveyed, of which, 174report having cell phones. Use a 5%level of significance. State the null and alternative hypothesis, find the p-value, state your conclusion, and identify the Type Iand Type IIerrors.

For statements a-j ( Section: 9.109 ), answer the following in complete sentences.

a. State a consequence of committing a Type I error.

b. State a consequence of committing a Type II error.

A random survey of 75 death row inmates revealed that the mean length of time on death row is 17.4 years with a standard deviation of 6.3 years. Conduct a hypothesis test to determine if the population mean time on death row could likely be 15 years.

a. Is this a test of one mean or proportion?

b. State the null and alternative hypotheses. H0: ____________________ Ha : ____________________

c. Is this a right-tailed, left-tailed, or two-tailed test?

d. What symbol represents the random variable for this test?

e. In words, define the random variable for this test.

f. Is the population standard deviation known and, if so, what is it?

g. Calculate the following:

i. x 炉 = _____________

ii. s = ____________

iii. n = ____________

h. Which test should be used?

i. State the distribution to use for the hypothesis test.

j. Find the p-value.

k. At a pre-conceived 伪 = 0.05, what is your:

i. Decision:

ii. Reason for the decision:

iii. Conclusion (write out in a complete sentence):

You flip a coin and record whether it shows heads or tails. You know the probability of getting heads is 50%, but you

think it is less for this particular coin. What type of test would you use?

A sleeping bag is tested to withstand temperatures of-15掳F. You think the bag cannot stand temperatures that low. State the Type I and Type II errors in complete sentences.
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