Question

Consider a significance test for a null hypothesis versus a two-sided alternative. Give a value of z (±0.001) that will give a result significant at the 4 % level but not at the 2 % level.

Answer #1

Consider a significance test for a null hypothesis versus a two-sided alternative. Give a value of z (±0.001) that will give a result significant at the 4 % level but not at the 2 % level. We use standard normal table to solve this.

The value of z at 4% level of significance is when alternative is two sided

z_{0.04/2} = z_{0.02} = -2.053

z is symmetric in nature, so, z_{0.98} = 2.053

The value of z at 2% level of significance is when alternative is two sided

z_{0.02/2} = z_{0.01} = -2.326

z is symmetric in nature, so, z_{0.99} = 2.326

So, z-value is in the interval -2.326<z<-2.053 or 2.053<z<2.326, it will be significant at 4% level but not at the 2% level.

question 1
1)
Consider a significance test for a null hypothesis versus a
two-sided alternative. State all values of a standard normal test
statistic z that will give a result significant at the 10%
level but not at the 5% level of significance. (Sec. 6.2)
You perform 1,000 significance tests using α = 0.01.
Assuming that all the null hypotheses are true, how many of the
test results would you expect to be statistically significant?
Explain your answer. (Sec. 6.3)...

For the following settings, test the null hypothesis that
theslope is zero versus the two-sided alternative.
a. n=20, yˆ=28.5 + 1.4x, and SEb1= 0.65.
Also need to find the margin of error for a 95% confidence
interval.

Suppose you have a two sided hypothesis test, Ha:
? ? ?0 with a test statistic
z=2.70. Determine the p-value and give the decision of
this test. Use a 5% level of significance.
a) P-value of 0.0035, reject the null hypothesis.
b) P-value of 0.0035, fail to reject the null hypothesis.
c) P-value of 0.9931, fail to reject the null hypothesis.
d) P-value of 0.0069, reject the null hypothesis.

If a two-sided null hypothesis is not rejected for a single mean
at a given significance level, the corresponding one-sided null
hypothesis (i.e., the same sample size, the same standard deviation
and the same mean) will _________ be rejected at the same
significance level.
A. Always
B. Sometimes
C. Never

1b. The p-value for a t test of a null hypothesis against a two
sided alternative is 0.00010578. The degrees of freedom are 45.
Which of the following is correct concerning the possible values
for the t statistic?
a. The t statistic could be 2.5 or -2.5
b. The t statistic can only be 2.5
c. The t statistic can only be -2.5
d. We need more information to determine the value of the t
statistic.

Conduct a test at the alphaequals0.10 level of significance by
determining (a) the null and alternative hypotheses, (b) the
test statistic, and (c) the P-value. Assume the samples were
obtained independently from a large population using simple random
sampling. Test whether p 1 greater than p 2. The sample data are x
1 equals 123, n 1 equals 248, x 2 equals 141, and n 2 equals
312. (a) Choose the correct null and alternative hypotheses below.
A. Upper H...

2. Given the null and alternative hypotheses and the test
statistics provided, compute the p-value for each of the following
hypothesis testing scenarios. If the tests are conducted at 5%
level of significance, what will be your decisions in each
case?
a. Ho: µ = 1346 versus Ha: µ ≠ 1346 and test statistic Z* =
2.30
b. Ho: µ ≥ 4000 versus Ha: µ < 4000 and test statistic Z* =
-1.80
c. Ho: µ ≤ 24.78 versus Ha:...

Using the critical value rule, if a two-sided null hypothesis
cannot be rejected for a single mean at a given significance level,
then the corresponding one-sided null hypothesis (i.e., the same
sample size, the same standard deviation, and the same mean) will
______________ be rejected at the same significance level.
a. never
b. sometimes
c. always

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...

Conduct a test at the alphaαequals=0.05 level of significance by
determining (a) the null and alternative hypotheses, (b) the
test statistic, and (c) the P-value. Assume the samples were
obtained independently from a large population using simple random
sampling.
Test whether p1>p2. The sample data are x1=128, n1=246,
x2=134,n2=312.
(b) Determine the test statistic.
z0=
(Round to two decimal places as needed.)
(c) The P-value depends on the type of hypothesis test. The
hypothesis test H0: p1=p2 versus H1: p1>p2...

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