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Chapter 7: Q9 (page 350)

Critical Value Refer to Exercise 7 “Requirements” and assume that the requirements are satisfied. Find the critical value that would be used for constructing a 95% confidence interval estimate of μusing the t distribution.

Short Answer

Expert verified

The critical value for computing the 95% confidence interval estimate of the mean voltage level is equal to 2.201.

Step by step solution

01

Given information

Referring to Exercise 7 CQQ, a sample of size (n) equal to 12 smartphone batteries is considered to estimate the mean voltage level. The confidence level is given to be equal to 95%.

02

Value of tα2

The confidence level is given to be equal to 95%. Thus, the level of significance αis equal to 0.05.

Now, the level of significance corresponding to the t-value is computed below:

α2=0.052=0.025

The value of the degrees of freedom is is calculated in the following manner:

df=n-1=12-1=11

Now, the value ofrole="math" localid="1648193070546" tα2for 11 degrees of freedom and 0.025 significance level is equal to 2.201.

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Most popular questions from this chapter

Finite Population Correction Factor If a simple random sample of size n is selected without replacement from a finite population of size N, and the sample size is more than 5% of the population size ,better results can be obtained by using the finite population correction factor, which involves multiplying the margin of error E by N-nN-1For the sample of 100 weights of M&M candies in Data Set 27 “M&M Weights” in Appendix B, we get x¯=0.8656 gands=0.0518 g First construct a 95% confidence interval estimate of , assuming that the population is large; then construct a 95% confidence interval estimate of the mean weight of M&Ms in the full bag from which the sample was taken. The full bag has 465 M&Ms. Compare the results.

Finding Sample Size Instead of using Table 7-2 for determining the sample size required to estimate a population standard deviation s, the following formula can be used

n=12zα2d2

where corresponds to the confidence level and d is the decimal form of the percentage error. For example, to be 95% confident that s is within 15% of the value of s, use zα2=1.96 and d = 0.15 to get a sample size of n = 86. Find the sample size required to estimate s, assuming that we want 98% confidence that s is within 15% of σ.

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Confidence Intervals. In Exercises 9–24, construct the confidence interval estimate of the mean. Arsenic in Rice Listed below are amounts of arsenic (μg, or micrograms, per serving) in samples of brown rice from California (based on data from the Food and Drug Administration). Use a 90% confidence level. The Food and Drug Administration also measured amounts of arsenic in samples of brown rice from Arkansas. Can the confidence interval be used to describe arsenic levels in Arkansas? 5.4 5.6 8.4 7.3 4.5 7.5 1.5 5.5 9.1 8.7

In Exercises 9–16, assume that each sample is a simplerandom sample obtained from a population with a normal distribution.

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