Question

Suppose Wall Street securities firms paid out year-end bonuses of $125,500 per employee last year. We take a sample of employees at the ASBE securities firm to see whether the mean year-end bonus is greater than the reported mean of $125,500 for the population. You wish to test the following claim ( H a ) at a significance level of α = 0.005 . H o : μ = 125500 H a : μ > 125500 You believe the population is normally distributed and you know the standard deviation is σ = 2600 . You obtain a sample mean of ¯ x = 126332.7 for a sample of size n = 39 . What is the test statistic for this sample? test statistic = (Report answer accurate to 3 decimal places.) What is the p-value for this sample? p-value = (Report answer accurate to 4 decimal places.) The p-value is... less than (or equal to) α greater than α This test statistic leads to a decision to... reject the null accept the null fail to reject the null As such, the final conclusion is that... There is sufficient evidence to warrant rejection of the claim that the population mean is greater than 125500. There is not sufficient evidence to warrant rejection of the claim that the population mean is greater than 125500. The sample data support the claim that the population mean is greater than 125500. There is not sufficient sample evidence to support the claim that the population mean is greater than 125500.

Answer #1

To test against

Here

sample mean

population standard deviation

and sample size

The test statistic can be written as

which under H_{0} follows a standard norma
distribution.

We reject H_{0} at 0.5% level of significance if P-value
< 0.005

Now,

The value of the test statistic

P-value

Since P-value = 0.022746 > 0.005, so we fail to reject
H_{0} at 0.5% level of significance and we can conclude
that **there is not
sufficient sample evidence to support the claim that the population
mean is greater than 125500**

You wish to test the following claim ( H 1 ) at a significance
level of α = 0.005 . H 0 : μ = 74.5 H 1 : μ > 74.5 You believe
the population is normally distributed, but you do not know the
standard deviation. You obtain a sample of size n = 15 with mean ¯
x = 86.8 and a standard deviation of s = 13.2 . What is the test
statistic for this sample? (Report...

You wish to test the following claim ( H a ) at a significance
level of α = 0.05 . H o : μ = 79.7 H a : μ > 79.7 You believe
the population is normally distributed, but you do not know the
standard deviation. You obtain the following sample of data: data
79.1 83.4 98.1 What is the test statistic for this sample? (Report
answer accurate to three decimal places.) test statistic = What is
the p-value...

You wish to test the following claim ( H a H a ) at a
significance level of α = 0.005 α = 0.005 . H o : μ = 64.4 H o : μ
= 64.4 H a : μ ≠ 64.4 H a : μ ≠ 64.4 You believe the population is
normally distributed, but you do not know the standard deviation.
You obtain the following sample of data: data 71.9 77.5 85.1 What
is the test statistic...

You wish to test the following claim ( H a Ha ) at a
significance level of α = 0.05 α=0.05 . H o : μ = 73.4 Ho:μ=73.4 H
a : μ > 73.4 Ha:μ>73.4 You believe the population is normally
distributed, but you do not know the standard deviation. You obtain
a sample of size n = 67 n=67 with mean M = 75.5 M=75.5 and a
standard deviation of S D = 13.4 SD=13.4 .
What is...

You wish to test the following claim ( H a ) at a significance
level of α = 0.005 . H o : μ = 77.3 H a : μ < 77.3 You believe
the population is normally distributed, but you do not know the
standard deviation. You obtain the following sample of data:
data
85.8
45.6
62.2
42.6
71.6
What is the test statistic for this sample? (Report answer
accurate to three decimal places.)
test statistic =
What is...

You wish to test the following claim ( H a ) at a significance
level of α = 0.002 .
H o : μ = 68.6
H a : μ ≠ 68.6
You believe the population is normally distributed, but you do
not know the standard deviation. You obtain a sample of size n = 11
with mean M = 65.9 and a standard deviation of S D = 15.2 .
What is the test statistic for this sample? (Report...

You wish to test the following claim ( H a ) at a significance
level of α = 0.02 .
H o : μ = 55.7 H a : μ ≠ 55.7
You believe the population is normally distributed, but you do
not know the standard deviation. You obtain a sample of size n =
111 with mean M = 50.4 and a standard deviation of S D = 14.8 .
What is the test statistic for this sample? (Report...

You wish to test the following claim ( H a ) at a significance
level of α = 0.02 . H o : μ = 59.2 H a : μ > 59.2 You believe
the population is normally distributed and you know the standard
deviation is σ = 7.3 . You obtain a sample mean of M = 61.6 for a
sample of size n = 50 .
What is the critical value for this test? (Report answer
accurate to...

You wish to test the following claim ( H 1 ) at a significance
level of α = 0.01 . H o : p = 0.78 H 1 : p > 0.78 You obtain a
sample of size n = 453 in which there are 377 successful
observations.
What is the test statistic for this sample? (Report answer
accurate to three decimal places.)
test statistic =
What is the p-value for this sample? (Report answer accurate to
four decimal places.)...

You wish to test the following claim ( H 1 ) at a significance
level of α = 0.005 . H o : p = 0.15 H 1 : p > 0.15 You obtain a
sample of size n = 412 in which there are 85 successful
observations. What is the critical value for this test? (Report
answer accurate to three decimal places.) critical value = What is
the test statistic for this sample? (Report answer accurate to
three decimal...

ADVERTISEMENT

Get Answers For Free

Most questions answered within 1 hours.

ADVERTISEMENT

asked 7 minutes ago

asked 11 minutes ago

asked 27 minutes ago

asked 33 minutes ago

asked 35 minutes ago

asked 38 minutes ago

asked 43 minutes ago

asked 44 minutes ago

asked 54 minutes ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago