74.1% of the respondents do actually prefer their gum. 29) What is the decision rule?
Reject H
0
if (
^
p
– P
0
) / √
P
0
(
1
−
P
0
)
/
n
¿
−
z
a
30) What are the null and alternative hypotheses for the test?
H
0
: P
0.80 and H
1
: P < 0.80 31) The value of the test statistic is:
-2.086
32) Consider the following probability distribution. Which of the following is true? x 0 1 2 3 4 5 6 P(x) 0.07 0.19 0.23 0.17 0.16 0.14 0.04
P(X
3 ) = 0.51 33) If conducting a two-sided test of population means, unknown variance, at level of significance 0.05 based on a sample of size 20, the critical t-value is:
2.093
34) What is the z-value for a two-sided test of hypothesis for a population mean when the probability of rejecting a true null hypothesis is equal to
.05?
1.960
A small community college claims that their average class size is equal to 35 students. This claim is being tested with a level of significance equal
to 0.02 using the following sample of class sizes: 42, 28, 36, 47, 35, 41, 33, 30, 39, and 48. Assume class sizes are normally distributed. 35) What is the value of the test statistic? 1.36
36) Which distribution is most appropriate to perform this hypothesis test?
Student's t distribution 37) Which of the following conclusions can be drawn? Since the test statistics equals 1.36, fail to reject the null hypothesis and conclude that
there's insufficient evidence to conclude that class size does not equal 35 students. To investigate the effectiveness of a diet, a random sample of 16 female patients is drawn from a population of adult females using the diet. The weight of each individual in the sample is taken at the start and at the end of the diet. Assume that the population of differences in weight before and after the diet follows a normal distribution. Suppose the mean decrease in weights over all 16 subjects in the study is 4.0 pounds with the standard deviation of differences computed as 6.4 pounds. Let µx - µy = mean weight before the diet - mean weight after the diet. 38) In order to test if the diet is effective, what is the appropriate alternative hypothesis? H
1
: µ
d
> 0
39) In order to test if the diet is effective, what is the value of the test statistic? 2.5
40) In order to construct a confidence interval estimate for the difference between two population means, independent samples are obtained from two normal populations with unknown but assumed to be equal variances. If the first sample contains 18 items and the second sample contains 14
items, which of the following distributions will be used? the t distribution with 30 degrees of freedom 41) A variable that can take on a finite and countable number of values is a A) discrete
variable.
The probability that a person catches a cold during the cold and flu season is 0.4. Assume that 10 people are chosen at random. 42) What is the standard deviation for the number of people catching a cold?
1.549
43) What is the probability that exactly four of them will catch a cold? 0.2508
44) An insurance company estimated that 30% of all automobile accidents were partly caused by weather conditions and that 20% of all automobile accidents involved bodily injury. Further of those accidents that involved bodily injury, 40% were partly caused by weather conditions. If a randomly chosen accident was partly caused by weather conditions, what is the probability that it involved bodily injury?
0.267 45) When testing for the difference between the means of two independent populations, with samples of sizes n1 and n2, where the population variances are unknown but assumed to be equal, what is the number of degrees of freedom?
n
1
+ n
2
- 2
46) Let the random variable Z follow a standard normal distribution. Find P(-2.21 < Z < 0). 0.4864 47) Investment A has an expected return of 7.8% with a standard deviation of 2%. Investment B has an expected return of 7.2% with a standard deviation of 3.1%. Which stock is more likely to have a return greater than 10%? Stock B
48) The t test for the difference between the means of two independent populations assumes that the respective:
populations are approximately normal.
A dependent random sample from two normally distributed populations gives the following results: n = 20, d = 26.5, s2 = 3.2 49) What is the lower confidence limit of the 98% confidence interval for the difference between the population means?
24.68
50) Suppose you have the following null and alternative hypotheses: H
0
: µ = 8.3 and H
1
: µ J 8.3. You take a sample of 30 observations, and find a sample mean of 7.3 with a standard deviation of 3.2. Which of the following is the most accurate statement about the p-value? 0.05 < p-value < 0.10
You have recently joined a Weight Watchers club. Suppose that the number of times you expect to visit the club in a month is represented by a normally distributed random variable with a mean of 12 and a standard deviation of 2.50. 51) Over the course of the next year, what is the probability that you average more than 13 visits to the club?
0.0823
52) If testing the difference between the means of two related populations with samples of sizes n1 = 16 and n2 = 16, what is the number of degrees of freedom?
15
The supervisor of a production line believes that the average time to assemble an electronic component is 14 minutes. Assume that assembly time
is normally distributed with a standard deviation of 3.4 minutes. The supervisor times the assembly of 14 components, and finds that the average time for completion is 11.6 minutes. 53) What are the appropriate null and alternative hypotheses?
H
0
: µ = 14 and H
1
: µ ≠
14
In a recent survey of 240 teachers in Richmond, Virginia, 77.2% supported standardized national testing of elementary students. In a survey of 162 teachers in Raleigh, North Carolina, 64.2% supported national testing. 54) What is the upper confidence limit of the 99% confidence interval for the difference between the two population proportions? 0.249
55) ^ The lower limit of a 95% confidence interval for the population proportion P given a sample size n = 100 and sample proportion p = 0.62 is equal to:
0.525
56) An insurance company estimated that 30% of all automobile accidents were partly caused by weather conditions and that 20% of all automobile accidents involved bodily injury. Further of those accidents that involved bodily injury, 40% were partly caused by weather conditions. What is the probability that a randomly chosen accident both was not partly caused by weather conditions and did not involve bodily injury?
0.58
