Question

The mean age of the patrons of a particular nightclub has historically been 35 years. The proprietor of the nightclub wishes to determine if the mean age of his patrons has changed. He uses a sample of 36 recent evenings and finds that the average age of the patrons in the sample is 36.8 years in the standard deviation of 3. 6 years. Let u be the mean of the patrons of the nightclub.

1) State the null and alternative hypothesis

2) Find the P value of the test. Give your answer to three decimal
places.

3) we conclude a x=5% that

Answer #1

a) As we are testing here that the mean has changed from 35 years, therefore the null and the alternate hypothesis here are given as:

b) The test statistic here is computed as:

Now as this is a two tailed test, for n-1 = 35 degrees of freedom, the p-value here is computed as:

p = 2P( t_{35} > 3 ) = 2*0.0025 = 0.005

**Therefore 0.005 is the required p-value
here.**

c) At a significance level of 5% that is 0.05, we see here that the p-value is 0.005 < 0.05, therefore the test is significant and we can reject the null hypothesis here and conclude that the mean has changed significantly from the mean of 35 years.

The mean age of the
patrons of a particular nightclub has historically been 35 years.
The proprietor of the nightclub wishes to find out if there is
evidence that the mean age of his patrons has increased. Let μ be
the mean age of the patrons of the nightclub.
Step 1: State the null
and alternative hypotheses.
Step 2: A random
sample of 41 recent evenings is selected. The average age of the
patrons in the sample is 36.4 years...

In the past, the average age of employees of a mid-sized
corporation has been 35 years. Recently, the company has been
hiring older individuals. In order to determine whether there has
been an increase in the average age of all the
employees, a sample of 64 employees was selected. The average age
in the sample was 45 years with a standard deviation of 16 years.
Let α = .05.
13. State the null and the alternative hypotheses.
14. Compute the...

In the past, the average age of employees of a mid-sized
corporation has been 35 years. Recently, the company has been
hiring older individuals. In order to determine whether there has
been an increase in the average age of all the employees, a sample
of 64 employees was selected. The average age in the sample was 45
years with a standard deviation of 16 years. Let α = .05.
13. State the null and the alternative hypotheses.
14. Compute the...

Suppose that the mean annual temperature in Asheville has
historically been 54.2 F. We take a sample of the last 10 years and
use that to decide if there is evidence that the mean annual
temperature has changed.
a. Write the null and alternative hypotheses for the hypothesis
test you would perform.
b. Describe what the Type I and Type II errors would be in this
situation.

One year, the mean age of an inmate on death row was 39.9
years. A sociologist wondered whether the mean age of a death-row
inmate has changed since then. She randomly selects 32 death-row
inmates and finds that their mean age is 38.3,with a standard
deviation of 8.1. Construct a 95% confidence interval about the
mean age. What does the interval imply?
A) Choose the correct hypotheses.
B) Construct a 95% confidence interval about the mean age.
The lower bound...

The mean age when smokers first start is 13 years old with a
population standard deviation of 1.8 years. A researcher thinks
that smoking age has significantly changed since the invention of
ENDS—electronic nicotine delivery systems. A survey of smokers of
this generation was done to see if the mean age has changed. The
sample of 34 smokers found that their mean starting age was 12.1
years old. Do the data support the claim at the 1% significance
level?
ho=...

One year, the mean age of an inmate on death row was 40.5
years. A sociologist wondered whether the mean age of a death-row
inmate has changed since then. She randomly selects 32 death-row
inmates and finds that their mean age is 39.5, with a standard
deviation of 8.6. Construct a 95% confidence interval about the
mean age. What does the interval imply? LOADING... Click the icon
to view the table of critical t-values. Choose the correct
hypotheses.
Upper H...

Historically, evening long-distance calls from a particular city
have averaged 15.2 minutes per call. In a random sample of 35
calls, the sample mean time was 14.3 minutes. Assume the standard
deviation is known to be 5 minutes. Using a 0.05 level of
significance, is there sufficient evidence to conclude that the
average evening long-distance call has decreased? Note: Use
the six-steps – clearly labeled (15 pts.)
State the null hypothesis and the alternative
hypothesis
Determine the critical value(s); (draw...

Historically, the proportion of adults over the age of 24 who
smoke has been .30. In recent years, much information has been
published and aired on radio and TV that smoking is not good for
one's health. A sample of 650 adults revealed only 23 percent of
those sampled smoked.
Develop a 98 percent confidence interval for the proportion of
adults who currently smoke. (Round your t-value to 2
decimal place and final answers to 3 decimal places.)
Confidence interval...

A sociologist is studying the age of the population in Blue
Valley. Ten years ago, the population was such that 19% were under
20 years old, 12% were in the 20- to 35-year-old bracket, 34% were
between 36 and 50, 23% were between 51 and 65, and 12% were over
65. A study done this year used a random sample of 210 residents.
This sample is given below. At the 0.01 level of significance, has
the age distribution of the...

ADVERTISEMENT

Get Answers For Free

Most questions answered within 1 hours.

ADVERTISEMENT

asked 1 minute ago

asked 18 minutes ago

asked 18 minutes ago

asked 18 minutes ago

asked 30 minutes ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago