Selected z* values from Table C:
For credit show or explain all answers.
1. (Round final answers to one decimal place.) A river passes through a small town. A scientist estimates the depth of the river where is passes through the town from a simple random sample of 20 measurements. She finds the average depth to be 5.2 feet. Suppose it is known the river’s depth through the town is distributed normally with a standard deviation (s ) of 2 feet.
(a) (5 pts.) Estimate the river’s depth through town with 95% confidence (i.e. Construct a 95% confidence interval).
(b) (5 pts.) Interpret the interval in part (a) above (i.e. say in words what it means).
(c) (5 pts.) How many measurements of the river’s depth would the scientist need to take if she wants to estimate its depth within a margin of error of ± .7 feet with 95% confidence?
(d). (5 pt.) If the scientist changed her level of confidence to 92%, what would be the critical value z*?
2. A researcher claims the yearly per person consumption rate of soft drinks is 52 gallons. In a simple random sample of 30 people, the mean of their yearly consumption is 54.3 gallons. The standard deviation (σ) of the population is 5.0 gallons. At the 5% level of significance, is this evidence the yearly soft drink consumption rate is different from 52 gallons per person? Carry out a test of significance to answer this question:
(a) (5 pts.) State your hypotheses using mathematical notation (symbols).
(b) (5 pts.) Calculate the value of the test statistic.
(c) (5 pts.) Determine the p-value.
(d) (5 pts.) State your conclusion in terms of the problem.
3. A study comparing body temperature between males and females was conducted.
Results are listed below:
Let and represent the mean body temperatures of all female and male responses, respectively.
- (5 pts) Does this data give evidence that male and female body temperatures differ?
- (5pts) Give a 90% confidence interval for . Interpret the interval.
State hypotheses, calculate the test statistic, approximate the P-value, and state your conclusion in terms of the problem.
Multiple Choice (1 pts. each)
1.Assume that event A occurs with probability 0.4 and event B occurs with
probability 0.5.Assume that A and B are disjoint events. Which of the following must be true?
a. It is possible that neither A nor B will occur.
b. If A occurs, then B does not occur.
c. The probability that A does not occur is 0.6.
d. All of the above
2. The central limit theorem says that when a simple random sample of size n is drawn from any population with mean m and standard deviation s, then when n is sufficiently large
a. the standard deviation of the sample mean is s2/n.
b. the distribution of the population is approximately Normal.
c. the distribution of the sample mean is approximately Normal.
d. the distribution of the sample mean is exactly Normal.
3. The P-value of the test of the null hypothesis is
a. the probability the null hypothesis is true.
b. the probability the null hypothesis is false.
c. the probability, assuming the null hypothesis is true, that the test statistic will take a value at least as extreme as that actually observed.
d. the probability, assuming the null hypothesis is false, that the test statistic will take a value at least as extreme as that actually observed.
4. You plan to construct a confidence interval for the mean µ of a Normal population with (known) standard deviation σ.Which of the following will reduce the size of the margin of error?
a. Use a higher level of confidence.
b. Increase the sample size.
c. Increase σ
d. All of the above.
5. You conduct a statistical test of hypotheses and find that the test is statistically significant at level a =0.05 with a
P-value=0.03.You may conclude that
a. the test would also be significant at level a = 0.10.
b. the test would also be significant at level a = 0.01.
c. both a and b are true.
d. neither a nor b is true.
6. If two variables, x and y, have a very strong linear relationship, then
a. there is evidence that x causes a change in y
b. there is evidence that y causes a change in x
c. there might not be any causal relationship between x and y
d. None of these alternatives is correct.
7. The correlation coefficient is used to determine:
a. A specific value of the y-variable given a specific value of the x-variable
b. A specific value of the x-variable given a specific value of the y-variable
c. The strength of the relationship between the x and y variables
d. None of these
8. If there is a very strong correlation between two variables then the correlation coefficient must be
a. any value larger than 1
b. much smaller than 0, if the correlation is negative
c. much larger than 0, regardless of whether the correlation is negative or positive
d. None of these alternatives is correct.
9. Sale of eggs that are contaminated with salmonella can cause food poisoning among consumers. A large
egg producer takes an SRS of 200 eggs from all the eggs shipped in one day. The laboratory reports that 11 of
these eggs had salmonella contamination. Unknown to the producer, 0.2% (two-tenths of one percent) of all
eggs shipped had salmonella. In this situation
a. 0.2% is a parameter and 11 is a statistic.
b. 11 is a parameter and 0.2% is a statistic.
c. both 0.2% and 11 are statistics.
d. both 0.2 % and 11 are parameters.
10. Which of the following statements are true?
I. The mean of a population is denoted by .
II. The population mean is a statistic.
(a) I only.
(b) II only.
(c) All of the above.
(d) None of the above.
11. A dietician claims that 60% of people in the U.S. are trying to avoid trans fats in their diets. You randomly select 100 people and find that 58 of them are trying to avoid trans fats. Use this information for questions (a) and (b) below.
(a) In a test of significance seeking evidence against the dietician’s claim, the alternative hypothesis is
A) Ha: p ≠ 58
B) Ha: μ ≠ 60
C) Ha: p ≠ 0.58
D) Ha: p ≠ 0.60
(b) Using the appropriate table, if the test statistic was -0.41 the p-value would be:
A) 0.25< p <0.5
C) p = 0.3409
D) p = 0.6818
12. SHOW WORK. An SRS of 18 recent birth records at the local hospital was selected. In the sample, the average birth weight was 119.6 ounces and the standard deviation was 6.5 ounces. Assume that in the population of all babies born in this hospital, the birth weights follow a Normal distribution, with mean . The standard error of the mean is
A) 6.50 ounces
B) 1.53 ounces
C) 0.36 ounces
D) 0.02 ounces
13. Do SAT coaching classes work? Do they help students to improve their test scores? Four students were selected randomly from all of the students that completed an SAT coaching class. For each student, we recorded their first SAT score (before the class) and their second SAT score (after the coaching class).
First SAT score
Second SAT score
To analyze these data we should use
A) the one-sample t test.
B) the matched pairs t test.
C) the two-sample t test.
D) Any of the above tests are valid. It just needs to be a t since is unknown.
14. In a test of significance, the P-value is
A) the probability the null hypothesis is true.
B) the probability the null hypothesis is false.
C) the probability, assuming the null hypothesis is true, that the test statistic will take a value at least as extreme as that actually observed.
D) the probability, assuming the null hypothesis is false, that the test statistic will take a value at least as extreme as that actually observed.
15. If conditions for inference were met and the true population standard deviation (σ) was known, the test statistic used for inference for a single true mean (μ) of a population is:
16. The variability of a statistic is described by
A) the spread of its sampling distribution.
B) the amount of bias present.
C) the vagueness in the wording of the question used to collect the sample data.
D) the stability of the population it describes.
17. You conduct a statistical test of hypotheses and find that the null hypothesis is statistically significant at level = 0.05. You may conclude that
A) the test would also be significant at level = 0.10.
B) the test would also be significant at level = 0.01.
C) both a and b are true.
D) neither a nor b is true.
18. The average age of residents in a large residential retirement community is 69 years with standard deviation 5.8 years.A simple random sample of 100 residents is to be selected, and the sample mean age of these residents is to be computed. We know the random variable has approximately a Normal distribution because of
a. the law of large numbers.
b. the 68-95-99.7 rule.
c. the central limit theorem.
d. the population we’re sampling from has a Normal distribution.
19. In a statistical test of hypotheses, we say the test is statistically significant at significance level if
a.the p-value of the test is less than or equal to
b.the p-value is greater than
c.the test statistic is less than or equalto
d.the p-value is less than or equal to .05
20. The sampling distribution of a statistic is
a.the probability that we obtain the statistic in repeated random samples.
b.the mechanism that determines whether randomization was effective.
c.the distribution of values taken by a statistic in all possible samples of the same size from the same population.
d.the extent to which the sample results differ systematically from the truth.
Select the word(s) from the following alphabetized list that best completes the sentences below, and write the word(s) in the blank space provided.
Word list: bias, categorical, confounding, correlation, distribution, experimental, explanatory, factor, frequency, p-value, inference, margin of error, probability, quantitative, regression, robust, response, sampling, standard error, simple random sample, treatments, variability, z-score, stratified random sample, observational study.
- (1 pt) The______________ of any outcome of a random phenomenon is the proportion of times the outcome would occur in a very long series of repetitions.
- (1 pt) The probability, assuming that the null hypothesis is true, that the test statistic would take a value as extreme or more extreme than that actually observed is called the ________________ of the test.
- (1 pt) Statistical ______________ provides methods of drawing conclusions about a population from sample data.
- (1 pt) A ___________ of size n consists of n individuals from the population chosen is such a way that every set of n individuals has an equal chance to be sample actually selected.
- (1 pt) A ______________ line is a straight line that describes how a response variable y changes as an explanatory variable x changes.
- (1 pt) The ____________ of a variable tells us what values the variable takes and how often it takes these values.
- (1 pt) When the standard deviation of a statistic is estimated from data, the result is called the ____________ of the statistic.
- (1 pt) The _______________ measures the direction and strength of linear relationship between two quantitative variables.
- (1 pt) ________________ variable measures an outcome of study.
- (1 pt) ______________ variable may explain or influence changes in ____________ variable.
- (1 pt) ______________ observes individuals and measures variables of interest but does not attempt to influence the responses; The purpose is to describes some group or situation.
- (1 pt) __________ Analysis (FA) is an exploratory technique applied to a set of observed variables that seeks to find underlying factors (subsets of variables) from which the observed variables were generated.
- (1 pt) __________ design is the branch of statistics that deals with the design and analysis of experiments. The methods of __________ design are widely used in the fields of agriculture, medicine, biology, marketing research, and industrial production.
- (1 pt) “randomization”: The random allocation of experimental units to experimental __________ . To allocate at random, each unit must have had the same chance of receiving any of the possible __________ .
- (1 pt) __________ variable: a variable that varies with a proposed explanatory variable and therefore whose effect it cannot be separated from.