Question

18. With statistical power of 95%, the researcher knows that in general
(a) the chance that the alternative hypothesis is true is 95%
(b) the P-value for the study will be 5%
(c) the chance that the null hypothesis is false is 5%
(d) there is a 95% chance that H0 will be rejected if it is not true.

19. A z-score indicates how many standard deviations a value is above or below the mean.
(a) True (b) False

Use for questions 20 - 22. The U.S. Fish and Wildlife Service reported that the mean length of
six-year-old rainbow trout in the Arolik River in Alaska is 441 millimeters with a standard deviation
of 81 millimeters. Assume these lengths are normally distributed.
20. What is the probability the length of a six-year-old rainbow trout is less than 400?
(a) 0.51 (b) 0.3050 (c) 0.6950 (d) -0.51

21. What is the probability the mean length of 30 six-year-old rainbow trout is less than 400?
(a) 0.3050 (b) 0.9972 (c) 0.0028 (d) 0.6950

22. What is the length of a six-year-old rainbow trout that is at the 80th percentile?
(a) 457.20 (b) 505.80 (c) 372.96 (d) 509.04

23. A psychologist is concerned about the health of veterans returning from war. She examines 20 veterans
and assesses whether they show signs of post-traumatic stress disorder. What is the sample of interest?
(a) All veterans returning from war. (b) The 20 veterans examined.
(c) All psychologists. (d) Veterans with post-traumatic stress disorder.

24. Is the underlined value a parameter or statistic? In a recent poll, 57% of the respondents supported a
school bond issue.
(a) Statistic (b) Parameter

25. According to the Internal Revenue Service, the proportion of federal tax returns for which no tax was
paid was 32.6%. As part of a tax audit, tax officials draw a simple random sample of 120 tax returns.
What is the probability that the sample proportion of tax returns for which no tax was paid is greater
than 40%?
(a) 0.0418 (b) 0.0495 (c) 0.9505 (d) 0.9582

Answer 1

As per company policies, I am answering 4 parts only.

18)

The statistical power of 95% means the probability of committing error i.e there is a 5%chance to reject H0 even though it is true.therefore the p-value for the study will be 5%.
(b) the P-value for the study will be 5%

19)

A z score indicates how many sd above or below mean. A + z score means the corresponding score is above mean. and a negative z score means that the corresponding score is below mean. Z score = (X-mean)/sd
(a) True

20)

P( X<400) = ?
I know that, z = (X-mean)/(sd)  
z1 = (400-441)/81) = -0.5062
hence, P(X<400) = P(Z<-0.5062)
P(X<400) = NORMSDIST(-0.5062)
P(X<400) = 0.3064
(b) 0.3050

21)
P(X < 400) = ?
I know that, z = (X-mean)/(sd/sqrt(n))  
z1 = (400-441)/81/sqrt(30))  
z1 = -2.7724
  
hence, P(X < 400) = P(Z<-2.7724)  
P(X < 400) = NORMSDIST(-2.7724)  
P(X < 400) = 0.0028  
(c) 0.0028

22)
P(Z<z) =   80%
z=   NORMSINV(0.8)
z=   0.841621234
I know that, z = (X-mean)/sd  
(X-mean)/sd =   0.8416
X=    0.8416*81+441
X=    509
(d) 509.04