Can someone please help with these 6 questions?
5. The distribution of the lengths of pregnancies in human
beings is roughly bell-shaped with mean 268 days and standard
deviation 7 days. The proportion of pregnancies that last at least
one week, i.e., seven days, longer than the average is about
(a) 0.16 (b) 0.68 (c) 0.84 (d) 0.50 (e) 0.32
6. Francesca is allergic to food additive A and to food additive
B. If 22% of all restaurant dishes contain additive A, 17% contain
additive B, and 8% contain both, then the probability that a
randomly selected dish will contain at least one of the two
additives, hence be inedible for Francesca, is about
(a) 0.39 (b) 0.04 (c) 0.47 (d) 0.31 (e) 0.13
20. In a random sample of 325 former prisoners in North
Carolina, 29% were arrested again within one year. A 90% confidence
interval for the proportion of all North Carolina prisoners who are
arrested again within one year is about:
(a) 0.29 ± 0.05 (b) 0.29 ± 0.06 (c) 0.29 ± 0.03 (d) 0.29 ± 0.07
(e) 0.29 ± 0.04
21. In the context of the previous problem, suppose that the
confidence interval obtained is too wide. Making use of the
information provided in that problem, the minimum sample size
required in order to estimate the same population proportion to
within two percentage points, still at 90% confidence, is
about:
(a) 684 (b) 1393 (c) 481 (d) 894 (e) 1108
25. In a test of hypotheses H0 : p = 0.42 versus Ha : p
0.42 at the 1% level of
significance a sample of size 1250 produced = 0.39 and test statistic z =
−2.149. The p-value (the observed significance) of the test is
about:
(a) 0.39 (b) 0.03 (c) −2.15 (d) −0.03 (e) 0.42
26. Knowing that drowsiness on the job significantly affects
productivity, the management of a large manufacturing firm
contemplates instituting an expensive program to encourage
employees to get sufficient sleep at night. To test the efficacy of
the program before a full-scale launch, they count the mean number
of quality control rejections per day of manufactured goods on 60
randomly selected days before the inception of a pilot program,
then count the mean number of quality control rejections per day of
goods on 30 days after its inception. The appropriate formula for
the test statistic in the relevant test of hypotheses is:
