Question

1.For testing H0 : p = 0.5 vs. Ha : p < 0.5 at level α, let a sample of size n = 100 is taken. What would be an appropriate rejection region?

A. t0 < tα B. z0 < zα C. z0 > zα D. |z0| > zα/2

2. A test statistic

A. is a function of a random sample used to test a hypothesis. B. is a function of a parameter used to test a hypothesis. C. is a fixed quantity. D. doesn’t have a probability distribution. 2

3. The output voltage for a certain electric circuit is specified to be 130. A sample of 40 independent readings on the voltage for this circuit gave a sample mean of 128.6 and a standard deviation of 2.1. Test the hypothesis that the average output voltage is 130 against the alternative that it is less than 130. Use a 5% significance level.

4. For a certain type of electronic surveillance system, the specifications state that the system will function for more than 1,000 hours with probability at least 0.90. Checks on 40 such systems show that 5 failed prior to 1,000 hours of operation. Does this sample provide sufficient information to conclude that the specification is not being met? Use α = 0.01.

Answer 1

Q1: We will perform a left tailed z test.

Answer: B. z0 < zα

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Q2: Answer: A. is a function of a random sample used to test a hypothesis.

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Q3: x̅ = 128.6, σ = 2.1, n = 40

Null and Alternative hypothesis:

Ho : µ = 130

H1 : µ < 130

Critical value :

Left tailed critical value, z crit = NORM.S.INV(0.05) = -1.645

Reject Ho if z < -1.645

Test statistic:

z = (x̅- µ)/(σ/√n) = (128.6 - 130)/(2.1/√40) = -4.2164

p-value :

p-value = NORM.S.DIST(-4.2164, 1) = 0.0000

Decision:

p-value < α, Reject the null hypothesis

There is enough evidence to conclude the population mean is less than 130 at 0.05 significance level.

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Q4:

No, it does not conclude that specification is not being met.