Question

Two researchers, working independently, conduct the same hypothesis test with different samples. Each uses a significance level of 3%. The first researcher’s sample has a P-value of 0.7%; the second researcher’s sample has a P-value of 4.53%.Select the true statement(s) below. There may be more than one correct answer, you must have all correct answers in order to receive credit.
A. The first researcher's sample provides stronger evidence against the null hypothesis.
B. The first researcher would fail to reject the null hypothesis.
C. The second researcher would fail to reject the null hypothesis.
D. The second researcher's sample provides stronger evidence against the null hypothesis.
E. The second researcher would conclude that the null hypothesis is true.
F. The first researcher would conclude that the null hypothesis is true.
G. The first researcher would reject the null hypothesis.
H. The second researcher would reject the null hypothesis.

If the psychic truly has ESP, then she should be correct more than 20% of the time, meaning p>0.20p>0.20. This hypothesis was tested using a significance level of α=5α=5%.

The psychic was shown 240 cards, and identified the correct symbol 51 times. Assume this can be treated as a Simple Random Sample.

For all samples of size 240, the sample proportions p^p^ have a Standard Deviation of

The value test statistic for this sample is z =

Answer 1

Correct option is:

A. The first researcher's sample provides stronger evidence against the null hypothesis.

C. The second researcher would fail to reject the null hypothesis.

G. The first researcher would reject the null hypothesis.

2)

null Hypothesis:               Ho:   p		=	0.200
alternate Hypothesis:    Ha: p		>	0.200
for 0.05 level with right tailed test , critical z=			1.645
Decision rule :   reject Ho if test statistic z > 1.645
sample success x   =		51
sample size          n    =		240
std error   se =√(p*(1-p)/n) =		0.0258
sample proportion p̂ = x/n=		0.2125
test stat z =(p̂-p)/√(p(1-p)/n)=		0.48

from above p^ have a Standard Deviation =0.0258

The value test statistic for this sample is z = 0.48