Question

Hypothesis testing (one sample t test):

1)

H0: Mean = 7.5

HA: Mean not equal to 7.5

X Bar = 8.5, SD = 1.2. n = 670, confidence interval: 95%

2)

H0: Mean = 125

HA: Mean no equal to 125

X Bar = 135, SD = 15, n = 500, confidence interval: 95%

Answer #1

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...

A one-sample test of H0: μ = 125
against Ha: μ > 125 is carried out
based on sample data from a Normal population. The SRS of size
n = 15 produced a mean 132.8 and standard deviation
12.6.
What is the value of the appropriate test statistic?
Select one:
a. z = 2.40
b. t = 2.32
c. t = 2.40
d. z = 2.32
e. t = 1.76

(a) Name the t test used in hypothesis testing to
evaluate the mean observed in one sample.
(b) Who determines the level of confidence for an interval
conservative?

A sample mean, sample standard deviation, and sample size are
given. Use the one-mean t-test to perform the required hypothesis
test about the mean, μ, of the population from which the sample was
drawn. Use the critical-value approach. Show all work carefully on
paper, include a graph, and fill in the blanks below.
x-bar = 21, s = 7.4, n = 11, H0: μ = 18.7, Ha: μ ≠ 18.7, α =
0.05

The following information is given for a one-sample t test: H0:
μ = 100; HA: μ < 100 Sample statistics: x̅= 95; s = 12.42 Value
of the test statistic: t = –1.80 (a) Determine the sample size, n.
(b) At a significance level α = 0.05, would your decision be to
reject H0 or fail to reject H0?

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...

A sample mean, sample size, and sample standard deviation are
provided below. Use the one-mean t-test to perform the required
hypothesis test at the 5% significance level.
X=25 s=9 n=24 H0: u=24 Ha: u>24

Consider the following hypothesis test.
H0: μ = 15
Ha: μ ≠ 15
A sample of 58 provided a sample mean x = 14 and a
sample standard deviation s = 6.3.
(a) Compute the value of the test statistic.
(b) Use the t distribution table to compute a range for
the p-value.
(c) At α = 0.05, what is your conclusion?
(d) What is the rejection rule using the critical value? What is
your conclusion?

5. Consider the hypothesis test H0 : μ = 18, Ha :μ ≠ 18. A
sample of size 20 provided a sample mean of 17 and a sample
standard deviation of 4.5.
a. 3pts.Compute the test statistic.
b.3pts. Find the p-value at the 5% level of significance, and
give the conclusion.
c. 5pts.Make a 99% confidence interval for the population
mean.
d. 5pts.Suppose you have 35 observations with mean17 and S.d.
4.5. Make a 90% confidence interval for the population...

Suppose that you are testing the hypotheses H0: μ=12 vs. HA:
μless than<12. A sample of size 25 results in a sample mean of
12.5 and a sample standard deviation of 1.9. a) What is the
standard error of the mean? b) What is the critical value of t*
for a 90% confidence interval? c) Construct a 90% confidence
interval for μ. d) Based on the confidence interval, at
alphaαequals=0.05 can you reject H0? Explain.

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