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
Clara has a package of six cookies she wants to share equally among her friends.
gladu [14]
She would atleast have 30 friends
8 0
3 years ago
Help me with this question
r-ruslan [8.4K]

Answer: 3/2a3

I can't properly write the answer sorry but it's the last one.

6 0
2 years ago
Read 2 more answers
Coefficient of x in -9xy2z is
andrew11 [14]

Answer:

The coefficient is -9

Step-by-step explanation:

The coefficient is the number that is multiplied by a variable and is always located before the variable.

7 0
3 years ago
______x 1/6 =5<br><br> Help pls and thx
arsen [322]
30 because 30 times 1/6 is 5
7 0
2 years ago
Read 2 more answers
What is (x - 3)2 + 2x - 4 for x=5 ?
yuradex [85]

Answer:

(x - 3)2 + 2x - 4 \\ (5 - 3)2 + 2 \times 5 - 4 \\ (2) \times 2 + 10 - 4 \\ 4 + 10   - 4 \\ 14 - 4 = 10

7 0
3 years ago
Other questions:
  • Katelyn plans to apply for a $10,000 loan at an interest rate of 5.6% for 5 years. Use the monthly payment formula to complete t
    6·1 answer
  • There are 240 seventh graders at yorktown middle school. Two thirds of the student participate in after school activities how ma
    12·1 answer
  • The sum of two numbers is 65. The larger number is 23 more than the smaller number . What are the numbers ?
    9·1 answer
  • If a runner has 20 ice trays and one is purple what is the answer
    10·1 answer
  • Choose the value of x that makes the open sentence true 40-x^2 &lt; 2x+15.
    7·2 answers
  • A car has a gasoline
    8·1 answer
  • How many solutions does 2x = 2x -9 have?
    13·1 answer
  • Which expression is equivalent to 2(d + 7)? ASAP PLEASE
    13·2 answers
  • Jinny is selling bracelets for $2.00. So far, she has earned $180.00. She needs to earn more than $228.00 in order to meet her g
    14·2 answers
  • Which expression has a conflict of 10 and a constant of5
    13·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!