Exam 1

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Question #1

Choose the explanation below that is correct.

A With large sample size, even small differences between the null value and the point estimate can be statistically significant.

B If the mean and the median of the data are 60.6 and 1.5, the distribution is negatively skewed.

C The total area under a normal density curve depends on the mean and standard deviation.

D Standard normal distribution is a normal probability distribution that has a mean of 1 and a standard deviation of 1.

Question #2

The standard error of p^ will be smaller when n=25 compare to when n=50.

A True

B False

Question #3

The distribution of the number of eggs laid by a certain species of hen during their breeding period has a mean of 35 eggs with a standard deviation of 18.2. Suppose a group of researchers randomly samples 100 hens of this species, counts the number of eggs laid during their breeding period, and records the sample mean. They repeat this 500 times, and build a distribution of sample means. What is the variability of this distribution?

A 18.2100=0.182

B 18.2500=0.0364

C 18.2100=1.82

D 18.2500=0.814

E 18.2

Question #4

147 college students are asked the question: “For how many days during the past 30 days was your mental health, which includes stress, depression, and problems with emotions, not good?” in Spring 2020. Based on responses, the survey reported a 95% confidence interval of 8.40 to 10.24 days in 2020. If a new survey were to be done with 500 college students, would the standard error of the estimate be larger, smaller, or about the same. Assume the standard deviation has remained constant since 2020.

A The standard error of the estimate would be larger

B The standard error of the estimate would be about the same

C The standard error of the estimate would be smaller

Question #5

Suppose the average number of deaths attributed to hyphoid fever over a 6-month period in a population is 2.3. Let X = the number of deaths attributed to hyphoid fever over a 1-year period. Which distribution does X follow?

A Poisson distribution

B Binomial distribution

C Normal distribution

Question #6

From the Question 11, determine the probability that none of them had a side effect.

A 0.859

B 0.774

C 0.97

D 0.026

E 0.030

Question #7

(Question 11 and 12) Suppose five individuals were randomly and independently selected for the placebo group in a clinical trial. Let X be the number of individuals experiencing significant side effects after receiving the placebo treatment and the percentage of individuals experiencing significant side effects after receiving the placebo treatment is 3%. What kind of distribution does X follow?

A Binomial distribution

B Normal distribution

C Poisson distribution

Question #8

The average number of testing COVID-19 in a hospital is six per day. What is the probability that exactly 2 people will visit the hospital to get the COVID-19 test on a randomly selected day?

A 0.3292

B 0.012

C 0.1670

D 0.0446

Question #9

Suppose weights of the checked baggage of airline passengers follow a nearly normal distribution with mean 45 pounds and standard deviation 3.2 pounds. Most airlines charge a fee for baggage that weigh in excess of 50 pounds. Determine what percent of airline passengers incur this fee.

A 1.56%

B 0.05%

C 94.06%

D 5.94%

Question #10

The average adult male heights in the US is 70 inches with a standard deviation of 3.3 inches. Suppose that the adult male heights closely follow a normal distribution. What value of the height will be the bottom 1.5%?

A 77.161 inches

B 74.950 inches

C 66.601 inches

D 62.839 inches

E 65.050 inches

Question #11

The average adult male heights in the US is 70 inches with a standard deviation of 3.3 inches. Suppose that the adult male heights closely follow a normal distribution. What is the probability that a randomly selected adult male in the US is between 69 inches and 74 inches?

A 0.5048

B 0.3821

C 0.4952

D 0.1131

E 0.8869

Question #12

Determine the type of study: A researcher obtains data about head injuries by examining hospital records from the past five years.

A Observational study – Cross-sectional

B Experimental design

C Observational study – Prospective

D Observational study – Retrospective

Question #13

A researcher is interested in the effects of exercise on mental health and he proposes the following study: Use stratified random sampling to recruit 18-30, 31-40, and 41-55 years old from the population. Next, randomly assign half the subjects from each age group to exercise twice a week, and instruct the rest not to exercise. Conduct a mental health exam at the beginning and at the end of the study, and compare the results between the groups with and without exercise. What type of study is this?

A Experiment because the researcher randomly assigned half the subjects to exercise.

B Observational study because the researcher used stratified random sampling.

C Experiment because the mental health exam is conducted at the beginning and at the end of the study.

D Observational study because three age groups are considered.

Question #14

Researchers collected data to examine whether there is any significant difference among different ethnic groups on body mass index (BMI). They also asked to report gender, marital status (single, married, widowed, divorced, separated, registered partnership), and socioeconomic status (lower, middle, upper). Measurement of the socioeconomic status is one of the variables in the study, and it is _____________.

A continuous

B discrete

C nominal

D ordinal

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