# Normal Probability, Hypothesis Testing & Confidence Interval

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From the book (Statistical Techniques in Business and Economics)

By D. A. Lind/ W. G. Marchal/ S. A. Wathen.

Chapter 8

1. Packages of sugar bags for Sweeter Sugar Inc. have an average weight of 16 ounces and a standard deviation of 0.24 ounces. The weights of the sugar bags are normally distributed. What is the probability that 16 randomly selected packages will have an average weight in excess of 16.08 ounces?

Chapter 9

2. A sample of 16 items yields X ̅ = 50 grams and s = 2.5 grams. Assuming a normal population distribution, construct a 95 percent confidence interval for the population mean weight.

3. Of a random sample of 600 trucks at a bridge, 120 had bad signal lights. Construct a 99 percent confidence interval for the percentage of trucks that had bad signal lights.

4. A cable TV company wants to estimate the percentage of cable boxes in use during an evening hour. A previous estimate is 25 percent. They want the estimate to be at the 95 percent confidence level and within 3 percentage points of the actual proportion. What sample size is needed?

Chapter 10

5. Test H0:   8 versus HA:  < 8, given =.01, n=36, =7.8 and s=.42. Assume the sample is selected from a normally distributed population.

6. Test H0: π  0.22 versus HA: π > 0.22 with p =.28 and n=144 at alpha=.01.

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#### Solution Preview

Please see the attachments.

From the book (Statistical Techniques in Business and Economics)

By D. A. Lind/ W. G. Marchal/ S. A. Wathen.

Chapter 8

1. Packages of sugar bags for Sweeter Sugar Inc. have an average weight of 16 ounces and a standard deviation of 0.24 ounces. The weights of the sugar bags are normally distributed. What is the probability that 16 randomly selected packages will have an average weight in excess of 16.08 ounces?

Answer

Let X be the weights of the sugar bags. Given that X is normal with mean µ = 16 and standard deviation = 0.24. Since X ~ N (µ, σ), . That is, or ~ N (16, 0.06). We need P ( > 16.08). Standardizing using and from standard normal tables, we have,

P ( > 77) = = P (Z > 1.3333) = 0.0912

Chapter 9

2. A sample of 16 items yields X ̅ = 50 grams and s = 2.5 grams. Assuming a normal population distribution, construct a 95 percent confidence interval for the population mean weight.

Answer

The 95% confidence interval is given by

Confidence Interval Estimate for the Mean

Data

Sample Standard Deviation 2.5

Sample Mean 50

Sample Size 16

Confidence Level 95%

Intermediate Calculations

Standard Error of the Mean 0.625

Degrees of Freedom 15

t Value 2.131449536

Interval Half Width 1.33215596

Confidence ...

#### Solution Summary

The solution provides step by step method for the calculation of normal probability, confidence interval and testing of hypothesis. Formula for the calculation and Interpretations of the results are also included. Interactive excel sheet is included. The user can edit the inputs and obtain the complete results for a new set of data.