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.

--

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.

--

Q4:

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

1. In testing a null hypothesis H0 versus an alternative Ha, H0
is ALWAYS rejected if
A. at least one sample observation falls in the non-rejection
region.
B. the test statistic value is less than the critical value.
C. p-value ≥ α where α is the level of significance. 1
D. p-value < α where α is the level of significance.
2. In testing a null hypothesis H0 : µ = 0 vs H0 : µ > 0,
suppose Z...

We wish to test the hypotheses H0: p=0.5 versus
Ha: p<0.5 at a 1% level of significance. Here, p
denotes the fraction of registered voters who support a proposed
tax for road construction. In order to test these hypotheses a
random sample of 500 registered voters is obtained. Suppose that
240 voters in the sample support the proposed tax. Calculate the
p-value. Do not included a continuity correction in the
calculation.

1. For testing H0 : µ = 0 vs. Ha : µ > 0, H0 is rejected if X
>¯ 1.645, given n = 36 and σ = 6. What is the value of α, i.e.,
maximum probability of Type I error?
A. 0.90 B. 0.10 C. 0.05 D. 0.01
2. For testing H0 : µ = 0 vs. Ha : µ > 0, H0 is rejected if X
>¯ 1.645, given n = 36 and σ = 6. What...

7.
You wish to test the following at a significance level of
α=0.05α=0.05.
H0:p=0.85H0:p=0.85
H1:p>0.85H1:p>0.85
You obtain a sample of size n=250n=250 in which there are 225
successful observations.
For this test, we use the normal distribution as an approximation
for the binomial distribution.
For this sample...
The test statistic (zz) for the data = (Please show
your answer to three decimal places.)
The p-value for the sample = (Please show your
answer to four decimal places.)
The p-value is...
greater than...

Question 1
The p-value of a test H0: μ= 20 against the
alternative Ha: μ >20, using a sample of
size 25 is found to be 0.3215.
What conclusion can be made about the test at 5% level of
significance?
Group of answer choices
Accept the null hypothesis and the test is insignificant.
Reject the null hypothesis and the test is insignificant.
Reject the null hypothesis and the test is significant
Question 2
As reported on the package of seeds,...

I. Solve the following problem:
For the following data:
1, 1, 2, 2, 3, 3, 3, 3, 4, 4, 5, 6 n = 12
b) Calculate
1) the average or average
2) quartile-1
3) quartile-2 or medium
4) quartile-3
5) Draw box diagram (Box & Wisker)
II. PROBABILITY
1. Answer the questions using the following
contingency table, which collects the results of a study to 400
customers of a store where you want to analyze the payment
method.
_______B__________BC_____
A...

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