Statistics question help needed

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statisticsisawesome

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Apr 11, 2020
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Carpal tunnel syndrome is a painful wrist condition that can be treated with surgery or less invasively with wrist
splints. In a study of 180 patients with the condition, half had surgery and half used wrist splints. In the surgery
group, 65 patients showed improvement after three months while 42 of those who used wrist splints improved.
Is surgery more effective than the use of wrist splints for patients with this condition?
a)
Write appropriate hypotheses.
b)
Test the hypotheses, find the P-value
and state your conclusion
in plain English
. Use α = 0.01.
c)
Create a 98% confidence interval for the difference in
proportions of patients showing improvement, and
interpret your interval.
d)
Comment on your interval in relation to your conclusion from

Here are my answers below
a. H0: p1 = p2

Ha: p1 > p2

b. p1 = 65/90 and p2 = 42/90

p = (90*(65/90)) + 90 * (42/90))/(90+90)) = 0.59444

standard error = sqrt(0.59444*(1-0.59444))*((1/90) + (1/90)) = 0.0732

therefore z = ((65/90) - (42/90))/(0.0732)) = 3.491

P-value = 0.0002

Since the p-value is < alpha, reject the null hypothesis. Therefore we can conclude that surgery is more effective than wrist splints.

c. ((65/90) – (42/90)) +- 2.326 * sqrt(((65/90))(25/90))/((90)) + ((42/90))(48/90)/(90)))

= (0.091, 0.42)

Therefore we are 98% confident that the difference in in proportions of patients showing improvement is between 0.091 and 0.42

d. (65/90) - (42/90) = 23/90 = 0.2555

since 0.2555 is contained in the 98% confidence interval it confirms our answer to part (b) to reject the null hypothesis.


Are all my answers correct?
 
statisticsisawesome said:
Carpal tunnel syndrome is a painful wrist condition that can be treated with surgery or less invasively with wrist
splints. In a study of 180 patients with the condition, half had surgery and half used wrist splints. In the surgery
group, 65 patients showed improvement after three months while 42 of those who used wrist splints improved.
Is surgery more effective than the use of wrist splints for patients with this condition?
a)
Write appropriate hypotheses.
b)
Test the hypotheses, find the P-value
and state your conclusion
in plain English
. Use α = 0.01.
c)
Create a 98% confidence interval for the difference in
proportions of patients showing improvement, and
interpret your interval.
d)
Comment on your interval in relation to your conclusion from

Here are my answers below
a. H0: p1 = p2

Ha: p1 > p2

b. p1 = 65/90 and p2 = 42/90

p = (90*(65/90)) + 90 * (42/90))/(90+90)) = 0.59444

standard error = sqrt(0.59444*(1-0.59444))*((1/90) + (1/90)) = 0.0732

therefore z = ((65/90) - (42/90))/(0.0732)) = 3.491

P-value = 0.0002

Since the p-value is < alpha, reject the null hypothesis. Therefore we can conclude that surgery is more effective than wrist splints.

c. ((65/90) – (42/90)) +- 2.326 * sqrt(((65/90))(25/90))/((90)) + ((42/90))(48/90)/(90)))

= (0.091, 0.42)

Therefore we are 98% confident that the difference in in proportions of patients showing improvement is between 0.091 and 0.42

d. (65/90) - (42/90) = 23/90 = 0.2555

since 0.2555 is contained in the 98% confidence interval it confirms our answer to part (b) to reject the null hypothesis.


Are all my answers correct?
Click to expand...
Why do you doubt your answers?

At a first glance, these look correct.
 
My complaint would be that you state your null hypothesis as "p1= p2" without saying what "p1" and "p2" mean! There was mention of a "p" in the problem (without saying what it meant) but no "p1" or "p2".
 
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