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
Irina-Kira [14]
3 years ago
9

1).Calculate T, when sample mean is 120, population mean is 100, standard deviation is 20 and smaple size is 10 using levels of

confidence at 0.05. 2). Determine if the sample mean is significantly different from the population mean.
Mathematics
2 answers:
Sonbull [250]3 years ago
8 0

Answer:

t=\frac{120-100}{\frac{20}{\sqrt{10}}}=3.16  

p_v =2*P(t_{9}>3.16)=0.012  

If we compare the p value and a significance level assumed \alpha=0.05 we see that p_v so we can conclude that we can reject the null hypothesis, and the true mean is significantly different from 100 at 5% of significance.  

Step-by-step explanation:

Data given and notation

\bar X=120 represent the sample mean  

s=20 represent the standard deviation for the sample

n=10 sample size  

\mu_o =100 represent the value that we want to test  

\alpha represent the significance level for the hypothesis test.  

t would represent the statistic (variable of interest)  

p_v represent the p value for the test (variable of interest)  

State the null and alternative hypotheses to be tested  

We need to conduct a hypothesis in order to determine if the mean is different from 100, the system of hypothesis would be:  

Null hypothesis:\mu = 100  

Alternative hypothesis:\mu \neq 100  

Compute the test statistic  

We don't know the population deviation, so for this case 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".  

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

t=\frac{120-100}{\frac{20}{\sqrt{10}}}=3.16  

Now we need to find the degrees of freedom for the t distirbution given by:

df=n-1=10-1=9

Conclusion

Since is a tao tailed test the p value would be:  

p_v =2*P(t_{9}>3.16)=0.012  

If we compare the p value and a significance level assumed \alpha=0.05 we see that p_v so we can conclude that we can reject the null hypothesis, and the true mean is significantly different from 100 at 5% of significance.  

artcher [175]3 years ago
3 0

Answer:

The sample mean is significantly different from the population mean.

Step-by-step explanation:

Null hypothesis: The sample mean is the same as the population mean.

Alternate hypothesis: The sample is significantly different from the population mean

Test statistic (t) = (sample mean - population mean) ÷ (sd/√n) = (120 - 100) ÷ (20/√10) = 20 ÷ 6.32 = 3.16

n = 10

degree of freedom = n - 1 = 10 - 1 = 9

From the t-distribution table, critical value corresponding to 9 degrees of freedom and 5% significance level is 2.262

The test is a two tailed, therefore the region of no rejection of the null hypothesis lies between -2.262 and 2.262.

Conclusion:

Reject the null hypothesis because the test statistic 3.16 lies outside the region bounded by the critical values.

The sample mean is significantly different from the population mean.

You might be interested in
Help asap plz ill give a gold medal. the label on cars antifreeze claims to protect the car between -30celsius and 130celsius. t
irga5000 [103]
The inequality would start out looking like this:
-30\ \textless \  \frac{5}{9} (F-32)\ \textless \ 130
Now it's just a matter of solving the inequalities simultaneously. Get rid of the fraction by multiplying everything by 9:
-270\ \textless \ 5(F-32)\ \textless \ 1170
Then distribute the 5 into the parenthesis:
-270\ \textless \ 5F-160\ \textless \ 1170
Now add 160 everywhere:
-110\ \textless \ 5F\ \textless \ 1330
and finally divide everything by 5:
-22<F<266


4 0
3 years ago
Amanda is building a fence. She needs a pole to measure 4 5\6 feet from the ground. How can she write it as a fraction.
aleksklad [387]
4 5/6 would be your answer then you figure out how to take away  the whole number

6 0
3 years ago
Read 2 more answers
Explain how different forms of data representation assist business decision-makers in their jobs.
Sliva [168]

Answer: Managers in a corporate setting tend to view decision making differently than ... to each possible outcome (a formal representation of this is known as a decision tree ). ... Such principles, when used in decision making, can help the organization ... enabling users to translate raw data into a form useful for decision support.

Step-by-step explanation: google

4 0
3 years ago
Read 2 more answers
How do you find "a" in -10+a=6a-7a please help I do not know how to find what the answer is.
Sunny_sXe [5.5K]
-10 + a = 6a - 7a

Rearrange the left hand side

a - 10 = 6a - 7a

Simplify 6a - 7a

a - 10 = -a

Add a on both sides

2a - 10 = 0

Add 10 on both sides

2a = 10

Divide by 2 on both sides

a = 5
4 0
3 years ago
A person is looking from a car to the top of a building. The angle of elevation to the top of the building from the car is 32°.
prohojiy [21]
I truly don’t know the answer but i think it is 837 feet
8 0
3 years ago
Read 2 more answers
Other questions:
  • What is 67km 230 m + 11 km 879 m
    12·1 answer
  • Ricky earned $102 in 8 hours
    7·1 answer
  • In a chemistry class, 12 L of a 12% alcohol solution must be mixed with a 20% solution to get a 14% solution. How many liters of
    15·1 answer
  • The viewership of a television show has decreased form 5.1 million viewers to 3.5 million viewers per episode. Find the percent
    7·1 answer
  • 9m + 11 - 8m - 6 + 5
    5·1 answer
  • Analyze is the product of 0.4×1.8 greater than or less than 0.4?please explain to me
    8·1 answer
  • What is the value of x when g(h(x)) = 4?
    14·1 answer
  • What is the y-intercept of the equation: 3x+6y=42
    7·1 answer
  • please help I will give 25 points and brainliest to the person who helped I need to see the work though too not just answer thes
    6·2 answers
  • Can someone help me? i need my math grade to go up
    11·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!