How to solve confidence interval t- test?

[匿名]

2016-08-01 4:15 pm

更新1:

The traditional radiation treatment for patients with a certain type of cancer is effective in 70% of cases. A new treatment using a product derived from soybeans has been developed. 965 patients were treated and 692 were effectively treated with the soybean derivative. Do a hypothesis test to determine if the new treatment is more effective than the radiation treatment using α = 0.01.

回答 (1)

cidyah

2016-08-01 5:18 pm

p= 0.70 (proportion where treatment is effective)
mean = (965)(0.70) = 675.5
standard deviation = sqrt ( n p (1-p) ) = sqrt( 965)(0.70)(0.30) ) = 6.5235

t - critical value = 2.575
H0: μ = 675.5
HA: μ > 675.5

Sample mean = 692
Standard deviation = 6.5235
Standard error of mean = s / √ n
Standard error of mean = 6.5235 / √ 965
SE = 6.5235/31.0644
Standard error of mean 0.21
t = (xbar- μ ) / SE
t = (692-675.5) / 0.21
t = 78.5718
Confidence interval 692-(0.21)(2.575) and 692+(0.21)(2.575)

(691.46, 692.54)

692 lies on the interval so the new treatment is not more effective since we do not reject H0.

This question is very ambiguous.

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