Question

74. When the sample size is changed from 2500 to 900, what is the effect on the std. error?

	A.	The new std error is 9/25 times the old error
	B.	The new std error is 3/5 of the old error
	C.	The new std error is 5/3 of the old error
	D.	The correct answer is not among the choices.
	E.	The new std error is 25/9 of the old error

67.

The test statistic for a certain left sided hypothesis test is zo=.40. At the 10% significance level, which of the following is false?

	A.	The test is not statistically significant
	B.	P-value > significance level
	C.	The sample mean exceeds the mean stated in the null hypothesis
	D.	The correct answer is not among the choices.
	E.	There is sufficient evidence to reject the null hypothesis

68.

Based on n = 25 observations, an appropriate 95% confidence interval for μ has been calculated as ( -2.8, 2.42 ) from a population with a normal distribution. The hypotheses of interest are Ho: μ = 1 versus Ha: μ ≠ 1. Based on this confidence interval, which of the following is the best conclusion?

	A.	we cannot perform the required test because we do not know the value of the test statistic.
	B.	reject Ho at the 0.05 level of significance, conclude that the mean is different from 1.
	C.	we should not reject Ho at the 0.10 level of significance.
	D.	reject Ho at the 0.10 level of significance, conclude that the mean is different from 1.
	E.	do not reject Ho at the 0.05 level of significance, there is insufficient evidence that the mean is different from 1

Answer 1

74)

std error = σ/√n

old std error = σ/√2500 = σ/50

new std error = σ/√900 = σ/30

new std error / old std error = (σ/30)/(σ/50) = 5/3

So,

The new std error is 5/3 of the old error (option C)

67)

zo=.40

left tail test

p value = P(z< 0.40) = 0.6554 [excel function used : "=NORMSDIST(0.4)" ]

α=0.10

P-value > significance level , do not reject Ho

hence, test is not significant

so, answer is There is sufficient evidence to reject the null hypothesis

68)

since, 95% confidence interval contains the null hypothesis value of 1, so, null hypothesis is not rejected

hence, answer is

do not reject Ho at the 0.05 level of significance, there is insufficient evidence that the mean is different from 1