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
steposvetlana [31]
3 years ago
9

The degenerative disease osteoarthritis most frequently affects weight-bearing joints such as the knee. Two random samples from

two different age categories are collected, and the following summary data on stance duration is presented. It is assumed that both age categories have equal population (true) variances.
Age Category Sample Size Sample Mean Sample Standard Deviation
Age Category 1 13 810 67
Age Category 2 19 770 56

Test the hypothesis that the mean of age category 1 is greater than the mean of age category 2 at 5% significance level.
Calculate P-Value.
Mathematics
1 answer:
Vinvika [58]3 years ago
4 0

Answer:

t=\frac{(810-770)-0}{\sqrt{\frac{67^2}{13}+\frac{56^2}{19}}}}=1.771  

df=n_1 +n_2 -2=13+19-2=30  

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

p_v =P(t_{30}>1.771)=0.0434  

Comparing the p value with the significance level \alpha=0.05 we see that p_v so we can conclude that we have enough evidence to reject the null hypothesis, and the mean for group 1 is significantly higher than the mean for the group 2

Step-by-step explanation:

Data given

\bar X_{1}=810 represent the mean for sample 1  

\bar X_{2}=770 represent the mean for sample 2  

s_{1}=67 represent the sample standard deviation for 1  

s_{2}=56 represent the sample standard deviation for 2  

n_{1}=13 sample size for the group 2  

n_{2}=19 sample size for the group 2  

\alpha=0.05 Significance level provided

t would represent the statistic (variable of interest)  

Concepts and formulas to use  

We need to conduct a hypothesis in order to check if the mean for category 1 is higher than the mean for category 2, the system of hypothesis would be:  

Null hypothesis:\mu_{1}-\mu_{2}\leq 0  

Alternative hypothesis:\mu_{1} - \mu_{2}> 0  

We don't have the population standard deviation's, so for this case is better apply a t test to compare means, and the statistic is given by:  

t=\frac{(\bar X_{1}-\bar X_{2})-\Delta}{\sqrt{\frac{\sigma^2_{1}}{n_{1}}+\frac{\sigma^2_{2}}{n_{2}}}} (1)  

And the degrees of freedom are given by df=n_1 +n_2 -2=13+19-2=30  

t-test: Is used to compare group means. Is one of the most common tests and is used to determine whether the means of two groups are equal to each other.  

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

t=\frac{(810-770)-0}{\sqrt{\frac{67^2}{13}+\frac{56^2}{19}}}}=1.771  

P value  

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

p_v =P(t_{30}>1.771)=0.0434  

Comparing the p value with the significance level \alpha=0.05 we see that p_v so we can conclude that we have enough evidence to reject the null hypothesis, and the mean for group 1 is significantly higher than the mean for the group 2

You might be interested in
Please make this quick
AveGali [126]

Answer:

27

Step-by-step explanation:

3x3+2x9=27

8 0
2 years ago
Please help someone ​
Cerrena [4.2K]
37 because theres 32 plus 5 which makes it 37
5 0
3 years ago
A psychologist collects data on the time, w, in minutes, people walk each day and their scores, t ,on a stress test. The scores
Svetach [21]
The answer is the last one D that is the correct answer 
good lock!!!

7 0
3 years ago
Joe has an ice cream stand. last week he spent $85 for ice cream and supplies. he earned $125. what was his profit?
Elodia [21]

Answer:

40 dollars

Step-by-step explanation:

Profit is what he earned minus his costs

Profit = 125 -85

Profit = 40

3 0
2 years ago
Find the median of the set of data. 30, 16, 49, 25 <br><br>​
weeeeeb [17]

Answer:

16,25,30,49

25+30=55

55÷2=27.5

Step-by-step explanation:

median means the middle value of any set of data so first arrange the data into ascending order.

16, 25, 30, 49

the data is even so we take both the middle value , add it and divide it with 2

25+30=55

55÷2=27.5

4 0
3 years ago
Other questions:
  • Twenty more than half a number of 70.what is the number
    10·2 answers
  • There were 12,000 spectators in one section of the stadium. In that section, 55% had on red shirts and the rest had on white shi
    7·2 answers
  • Write 6/5 as a percent?
    7·2 answers
  • Lines AB, CD, and EF intersect at point G. How many PAIRS of vertical angles are there in this diagram
    6·1 answer
  • Can someone help me?
    14·1 answer
  • Show two methods you can use to convert 60 inches to centimeters
    8·2 answers
  • Susie purchases a $13,000 car and plans to repay the loan by making monthly payments over the course of five years. The interest
    8·2 answers
  • Use front-end rounding to estimate the sum:
    6·2 answers
  • Let D be the ordered set of all possible words (not just English words, all strings of letters of arbitrary length) using the La
    13·1 answer
  • Becky has borrowed money from two friends and she wants to pay off her debts. Her debt to one friend is represented by the numbe
    6·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!