Question

# 1) • z-value should be expressed to three decimal places: e.g., z=1.645. • Before you start...

1)

• z-value should be expressed to three decimal places: e.g., z=1.645.

• Before you start each question, you should determine if you are dealing with the population mean or proportion since what you do depends on the type of parameter at hand.

• When handling proportion problems, write/use/plug proportions as decimals (e.g., not 54%, but .54).

• In the beginning, state clearly if you do a 1-tailed or 2-tailed test. State clearly your H0 and H1 using correct Greek letters, mathematical symbols, and subscripts. Do not state your hypotheses in prose form. Express numbers to the three decimal places.

• Use Z test, not t test. Don’t use p-value. Articulate if you reject H0. Justify why you reject or FTR H0.

• After articulating your statistical decision, state clearly your research conclusion in prose form: do NOT use Greek letters, mathematical symbols, or subscripts for the research conclusion. Show all the relevant quantities (e.g., sample statistics, SE, Z-statistic, to name a few) and label them properly: don’t omit anything.

• At the end of your answer, compute and interpret the corresponding CI.

• Write the lower and upper bounds in the CI for μ to the two decimal places: e.g., [11.33, 15.55].

• Write the lower and upper bounds in the CI for π (or P) to the four decimal places: .e.g., [.3012, .3875].

1. A manufacturer of guitar amplifiers markets one of its models, Vagabond, at a power rating of 50 watts. GuitarGod magazine suspects that this rating is inaccurate for this year's model of the amp. In a random sample of 30 units of this year's version of the Vagabond, the mean output power is 48 watts, with a standard deviation of 8 watts. Assuming a confidence level of 95%, which is your conclusion?

We will use one sample z test as it is mentioned in the instructions that use z test not t test.

Null hypothesis Ho : u = 50

Alternate hypothesis H1 : u not equal to 50

This is two tailed test

Alpha = 0.05 (1 - 0.95)

As the test is two tailed we will first divide the alpha into two equal parts

0.05/2 = 0.025

From z table, P(z<-1.96) = p(z>1.96) = 0.025

That is critical values are -1.96 and 1.96 respectively

And rejection region is

Reject null hypothesis Ho if test statistics is greater than 1.96 or less than -1.96

Test statistics z = (sample mean - claimed mean)/(s.d/√n)

Z = (48-50)/(8/√30) = -1.369

As -1.369 is not less than -1.96

We fail to reject null hypothesis Ho

Confidence interval.

Critical value z = 1.96

Margin of error (MOE) = z*s.d/√n

MOE = 1.96*8/√30 = 2.86276323389

Confidence interval is given by

[Mean - MOE, Mean + MOE)

Mean = 48

[45.14, 50.86]

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