1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
kodGreya [7K]
3 years ago
13

The local oil changing business is very busy on Saturday mornings and is considering expanding. A national study of similar busi

nesses reported the mean number of customers waiting to have their oil changed on Saturday morning is 3.6. Suppose the local oil changing business owner, wants to perform a hypothesis test. The null hypothesis is the population mean is 3.6 and the alternative hypothesis is the population mean is not equal to 3.6. The owner takes a random sample of 16 Saturday mornings during the past year and determines the sample mean is 4.2 and the sample standard deviation is 1.4. It can be assumed that the population is normally distributed. The level of significance is 0.05. The decision rule for this problem is to reject the null hypothesis if the observed "t" value is _______.
Mathematics
1 answer:
eimsori [14]3 years ago
3 0

Answer:

t=\frac{4.2-3.6}{\frac{1.4}{\sqrt{16}}}=1.714

Reject the null hypothesis if the observed "t" value is less than -2.131 or higher than 2.131  

Rejection Zone: t_{calculated} or t_{calculated}>2.131

In our case since our calculated value is not on the rejection zone we don't have enough evidence to reject the null hypothesis at 5% of significance.

Step-by-step explanation:

Previous concepts  and data given  

The margin of error is the range of values below and above the sample statistic in a confidence interval.  

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".  

\bar X=4.2 represent the sample mean  

s=1.4 represent the sample standard deviation  

n=16 represent the sample selected  

\alpha=0.05 significance level  

State the null and alternative hypotheses.    

We need to conduct a hypothesis in order to check if the mean is different from 3.6, the system of hypothesis would be:    

Null hypothesis:\mu = 3.6    

Alternative hypothesis:\mu \neq 3.6    

If we analyze the size for the sample is < 30 and we know the population deviation so is better apply a t test to compare the actual mean to the reference value, and the statistic is given by:    

t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}  (1)    

t-test: "Is used to compare group means. Is one of the most common tests and is used to determine if the mean is (higher, less or not equal) to an specified value".    

Calculate the statistic  

We can replace in formula (1) the info given like this:    

t=\frac{4.2-3.6}{\frac{1.4}{\sqrt{16}}}=1.714

Critical values

On this case since we have a bilateral test we need to critical values. We need to use the t distribution with df=n-1=16-1=15 degrees of freedom. The value for \alpha=0.05 and \alpha/2=0.025 so we need to find on the t distribution with 15 degrees of freedom two values that accumulates 0.025 of the ara on each tail. We can use the following excel codes:

"=T.INV(0.025,15)" "=T.INV(1-0.025,15)"

And we got t_{crit}=\pm 2.131    

So the decision on this case would be:

Reject the null hypothesis if the observed "t" value is less than -2.131 or higher than 2.131  

Rejection Zone: t_{calculated} or t_{calculated}>2.131

Conclusion    

In our case since our calculated value is not on the rejection zone we don't have enough evidence to reject the null hypothesis at 5% of significance.

You might be interested in
What is 7.2 times 10^5 equal to.
FromTheMoon [43]
The answer to this is 720000
4 0
3 years ago
Read 2 more answers
What is the value of x so that the line segment with endpoints W(x, −2) and X(5, −4) is parallel to the line segment with endpoi
coldgirl [10]

Answer:

x equals six start fraction one over two end fraction

Step-by-step explanation:

Segments which are parallel have the same slope. Find the slope of of YZ. Then using that value, find the slope WX and solve for the value of x.

Slope of YZ is:

m = \frac{y_2-y_1}{x_2-x_1}=\frac{2-6}{2-5}=\frac{-4}{-3}=\frac{4}{3}

Since they are parallel, then WX has a slope of 4/3 too.

Slope of WX is:

m = \frac{y_2-y_1}{x_2-x_1}\\\\\frac{4}{3}=\frac{-2--4}{x-5}\\\\\frac{4}{3}=\frac{2}{x-5}\\\\\frac{4}{3} (x-5) = 2\\\\4x -20=6\\\\4x = 26\\\\x = 6\frac{1}{2}

5 0
2 years ago
1200 people visited a museum. 240 of the visitors were children. what percent of the visitors were children?​
sergeinik [125]

Answer:

20 percent

Step-by-step explanation:

To find the percentage that were children, we take the number of children over the total and multiply by 100%

There are 240 children and 1200 total people

240/1200 * 100%

.2*100%

20%

5 0
3 years ago
Read 2 more answers
6x - Зу = 12<br> What are the x and y intercept
bazaltina [42]

Answer:

x=6 y=-3

Step-by-step explanation:

4 0
2 years ago
Read 2 more answers
Find the percent change from 72 to 80.
LenaWriter [7]
11.1111 I think this is it
3 0
3 years ago
Other questions:
  • Flip a coin 4 times and calculate the experimental probability of the coin landing heads up.
    13·2 answers
  • If 5^x = 125, find the value of x
    12·2 answers
  • A 6th grade teacher can grade 25 homework assignments in 20 minutes. Is this working at a faster rate or slower rate than gradin
    14·1 answer
  • mary is eighteen years older than her son. she was three times as old as he was one year ago.How old are they now?
    12·1 answer
  • Solve for the unknown: g - 24 = 75
    9·1 answer
  • On a map, 1 in.represents 20 mi. Two cities are 3 1/2 in. apart on the map.How far apart are the actual cities
    13·2 answers
  • Plssss help. High school mathematics
    8·1 answer
  • 12, 21, 30 and 39 are the first four terms in a sequence
    13·1 answer
  • Need help ill pay a lot just do my math test. answer every question
    13·1 answer
  • Solve the equation. Then check your solution
    6·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!