Question

A school conducts survey of nine-hundred random students and results show that four-hudnred-eighty-five support Anna for class president. population proportion of surveyors --> "p"

test of... p= .5 vs p > .5

x= 485, n =900, sample p = .538889, 95% CI = (.506322, .571456), z-value = 2.33, p-val = .010

a. give the p-value for testing null hypothesis p=.5, against alt. hypothesis where p< .5?

b. give p-value for testing null hyp. p=.5, where alt hypothesis --> p ≠ .5 ?

c. give value of test statistic for testing null hyp. --> p=.56?

d. give p-value for testing null hyp --> p=.56, against alt. hypothesis p< .56

e. would null hyp. p=.56 be not chosen in favor of alt. hyp. p< .56 at test level of TEN percent?

Answer 1

a) p-value for one-sided test remains the same for each side. Hence p-value here also = 0.010

b) p-value for two-sided test = 2* p-value for one-sided test = 2*0.010 = 0.020

c)  Let's first find Standard error for the condition.

t-statistic corresponding to p-value of 0.538889 and degrees of freedom 484 is 1.612

=> SE = 0.024

Now this standard error will be used in finding new t-value for p = 0.56

= (0.539 - 0.56) / 0.024 = -0.875

d) give p-value for testing null hyp --> p=.56, against alt. hypothesis p < .56 is P(T < -0.875) = 0.8091

e) At test level of 10% or 0.1, we have p>0.1, so we fail to reject the null hypothesis.

The null hypothesis would be chosen and not rejected.