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

Vinvika [58]

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

4 0

3 years ago

In algebra how do i convert y-7=-2/3(x+1) into standard form and what would it be?

Art [367]

Answer:

C

Step-by-step explanation:

Where, if at all possible,

A

,

B

, and

C

are integers, and A is non-negative, and, A, B, and C have no common factors other than 1

8 0

3 years ago

A pair of trainers cost £60. In a sale they are reduced by 40%. What is the new price?

elena55 [62]

Answer:

36

Step-by-step explanation:

40 % of 60 = 24

60-24=36

8 0

2 years ago

What is the value of x

Pachacha [2.7K]

Answer:

x = 2

Step-by-step explanation:

3 0

3 years ago

If the null hypothesis of an experiment is “The true mean weight of the geese is greater than 40 pounds” what is the alternate h

Ira Lisetskai [31]

Answer:

"The true mean weight of the geese is less than or equal to 40 pounds"

Step-by-step explanation:

Something (or some value) can be either equal to, greater than, or less than another thing (another value).

Null Hypothesis is what is given and Alternate is what we are testing.

Since Null Hypothesis is given that the mean weight is GREATER THAN 40 pounds, the ALTERNATE HYPOTHESIS would be the mean weight is either EQUAL TO or LESS THAN 40 pounds.

Thus, alternate hypothesis is "The true mean weight of the geese is less than or equal to 40 pounds"

5 0

3 years ago