Question

Use minitab if possible. If it is please show step by step process of how you did it.

Amanufacturer is interested in the output voltage of a power supply used in a PC. Output voltage is assumed to be normally distributed with standard deviation 0.3 volt, and the manufacturer wishes to test Ho : u = 8 volts against Hiiu* & volts. Calculate the probability of a type Il error if the true mean output is 8.04 volts and round your answers to three decimal places (eg. 98.765). and n= 11 (a) a = 0.01 B = (b) a = 0.01 B = i and n = 15 (c) Compare the values of B calculated in the previous parts. What conclusion can you draw? As n increases, 3 decreases. As nincreases, B increases.

Answer 1

(a) Stat --> Power and sample size --> 1 sample Z

ill. Minitab - Untitled 13 File Edit Data Calc Stat Graph Editor Tools Window Help Assistant - Lule Power and Sample Size for 1-Sample Z: Options х XQ Alternative Hypothesis Less than Not equal Worksheet 2 Greater than C1 C7 Significance level: 0.01 + 1 2 Help OK Cancel 3 4 5 11 Specify values for any two of the following: Sample sizes: Differences: 0.04 Power values: 6 7 8 9 Standard deviation: 0.3 10 11 Options... Graph... 12 Help OK Cancel 13

Output:

Power and Sample Size 1-Sample 2 Test Testing mean = null (versus # null) Calculating power for mean = null + difference a = 0.01 Assumed standard deviation = 0.3 Results Difference 0.04 Sample Size Power 11 0.0177093

Ans : P(Type II Error) = 1-0.0177 = 0.982

(b)

Results Difference 0.04 Sample Size Power 15 0.0207

Ans : P(Type II Error) = 1-0.0207 = 0.9793

(c)

As n increases, ß decreases.