unit 8 statistics multiple choice review

a random sample of 100 votes in a community produced 59 voters in favor of candidate A.the observed value of the test statistic for testing the null hypothesis ho: p=0.5 versus the alternative hypothesis ha: p not= 0.5 is:

a 1.80

you want to design a study to estimate the proportion of students on your campus who agree with the statement, "the student government is an effective organization for expressing the needs of students to the administration." you will use a 95% confidence interval and you would like the margin of error of the interval to be 0.05 or less. the minimum sample size required is approximately

c. 385

a test of ho: mu=60 versus ha: mu not= 60 produces a sample mean of x=58 and a p-value of 0.04. at an alpha level of 0.05, which of the following is an appropriate conclusion?

e. there is sufficient evidence to conclude that mu not = 60

phoebe has a theory that older students at her high school are more likely to bring a bag lunch than younger students, because they have grown tired of cafeteria food. she takes a simple random sample of 80 sophomores and finds that 52 of them bring a bag lunch. a simple random sample of 104 seniors reveals that 78 of them bring a bag lunch. letting p1 be the proportion of sophomores who bring a bag lunch, and p2 be the proportion of seniors who bring a bag lunch, phoebe tests the hypotheses ho: p1-p2=0; ha: p1-p2<0 at the alpha level 0.05. phoebe's test statistic is -1.48. which of the following is closest to the appropriate p-value for the test?

a. 0.0694

a significance test was performed to test the null hypothesis ho: p=0.5 versus the alternative ha: p>0.5. the test statistic is z=1.40. which of the following is closest to the p-value for this test?

a. 0.0808

we want to test ho: mu=1.5 vs. ha: mu not= 1.5 at alpha level 0.05. a 955 confidence interval for mu calculated from a given random sample is (1.4, 3.6). based on this finding we

a. fail to reject ho

which of the following statements is/are correct? I. the power of a significance test depends on the effect size II. the probability of a type II error is equal to the significance level of the test III. error possibilities can be expressed only when a significance level has been specified

b. I and III only

the average time it takes for a person to experience pain relief from aspirin is 25 minutes. a new ingredient is added to help speed up relief. let mu denote the average time to obtain pain relief with the new product. an experiment is conducted to verify if the new product is better. what are the null and alternative hypotheses?

b. ho: mu=25 ha: mu<25

which of the following conditions must be met in order to use a t-procedure on these paired data?

b. only the distribution of differences (after 6 weeks-before) must be approximately normal

we wish to test ho that the average family income of Manitoba families is at least $15,000 at level of significance alpha=0.05. in order to test the null hypothesis a sample size of 1000 is selected from the population, and the p-value of the test is determined to be 0.02. we then:

b. reject ho because the data are sufficiently unusual if the null hypothesis were true

a group of nutritionists is hoping to prove that a new soy bean compound has more protein per gram than roast beef, which has a mean protein content of 20. a random sample of 5 batches of the soy compound have been tested, with the following results: protein content: 15 22 17 19 23 what assumption(s) do we have to make in order to carry out a legitimate statistical test of the nutritionists' claim?

b. the mean protein content of the 5 batches follows a normal distribution

following the analysis of some date on two samples drawn from populations in which the variable of interest is normally distributed, the p-value for the comparison of the two sample means under the null hypothesis that the two population's means are equal against the alternative hypothesis that the two population means are not equal was found to be 0.0063. this p-value indicates that:

b. there is rather strong evidence against the null hypothesis

we wish to test if a new feed increases the mean weight gain compared to an old feed. at the conclusion of the experiment it was found that the new feed gave a 10 kg bigger gain than the old feed. a two-sample t-test with the proper one-sided alternative was done and the resulting p-value was 0.082. this means:

b. there was only an 8.2 % chance of observing an increase greater than 10 kg (assuming the null hypothesis was true).

which of the following procedures is appropriate to test the hypothesis of equal average fat content in two types of ice cream?

b. two-sample t test with 4 df

an appropriate 95% confidence interval for mu has been calculated as (-0.73, 1.92) based on n=15 observations from a population with a normal distribution. the hypothesis of interest are ho: mu=0 versus ha: mu not= 0. based on this confidence interval,

b. we should not reject ho at the alpha level 0.05 level of significance

all of us nonsmokers can rejoice-the mosaic tobacco virus that affects and injures tobacco plants is spreading! meanwhile, a tobacco company is investigating if a new treatment is effective in reducing the damage caused by the virus. eleven plants were randomly chosen. on each plant, one leaf was randomly selected, and one half of the leaf (randomly chosen) was coated with the treatment, while the other half was left untouched (control). after two weeks, the amount of damage to each half of the leaf was assessed. for purposes of comparing the damage, which of the following is the appropriate type of procedure?

c. matched pairs t procedures

what would a type II error be for this test of the water diet?

c. not concluding that the diet leads to weight loss when it does

because t procedures are robust, the most important condition for their use is

c. the data can be regarded as a random sample from the population

the recommended daily calcium intake for women over 21 (and under 50) is 1000 mg per day. the health services at a college are concerned that women at the college get less calcium than that, so they take a random sample of female students in order to test the hypotheses ho: mu=1000 versus ha: mu<1000. prior to the study they estimate that the power of their test against the alternative ha: mu=900 is 0.85. which of the following is the best interpretation of this value?

c. the probability of rejecting the null hypothesis when the parameter value is 900

in a test of ho: p=0.4 against ha: p not = 0.4, a sample of size 100 produces z=1.28 for the value of the test statistic. thus the p-value of the test is approximately equal to:

d. 0.20

a researcher wishes to determine if people are able to complete a certain pencil and paper maze more quickly while listening to classical music. suppose previous research has established that the mean time needed for people to complete a certain maze (without music) is 40 seconds. the researcher, therefore, decides to test the hypotheses ho: mu=40 versus ha: mu<40, where mu is the time in seconds needed to complete the maze while listening to classical music. to do so, the researcher has 10,000 people complete the maze with classical music playing. the mean time for these people is x=39.92 seconds, and the p-value of this significance test is 0.0002. which statement below best describes the appropriate conclusion to draw from this study?

d. although the researcher has obtained a statistically significant result, it appears to have little practical significance

which of the following is INCORRECT about the use of a paired experiment?

e. because pairing is beneficial, we can pair all data by matching the smallest value of each sample, the second smallest value of each sample, the third smallest value of each sample, etc.