Question

***please use rstudio to answer question, I am unsure how to do these calculations with the program and do not need to know how to do them by hand***

Physicians at a clinic gave what they thought were drugs to 950 patients. Although the doctors later learned that the drugs were really placebos, 56 % of the patients reported an improved condition. Assume that if the placebo is ineffective, the probability of a patients condition improving is 0.55. Test the hypotheses that the proportion of patients improving is >0.55

Find the test statistic:

z= ___

Find the p-value.

p= ___

Answer 1

The R-studio output is ,

> #Given:
> n=950
> #'p' be the sample proportion
> p=0.56
> x=n*p
> x
[1] 532
> #Hypothesized value p0
> p0=0.55

> prop.test(x,n,p0,,correct=FALSE)

1-sample proportions test without continuity correction

data: x out of n, null probability p0
X-squared = 0.38384, df = 1, p-value = 0.2678
alternative hypothesis: true p is greater than 0.55
95 percent confidence interval:
0.5333765 1.0000000
sample estimates:
p
0.56

The test statistic is ,

The p-value is ,

p-value=0.2678

Decision : Here , p-value > 0.05 significance level

Therefore , fail to reject the null hypothesis.

Conclusion : Hence , there is not sufficient evidence to conclude that the proportion of patients improving is 0.55