Stats Test 3 Practice
What critical value should be used to construct a 90% confidence interval for the population mean when the population standard deviation is known?
z = 1.645
John performed a one-sample z-test for proportions and obtained a p-value of 0.35. John decided to reject the null hypothesis. What is the probability John made a Type I Error?
0.35
A hungry college student just finished eating a large cheese and pepperoni pizza from Doug's Pizza Palace and felt there wasn't enough cheese and pepperoni on it as he has had large pizzas with more cheese and pepperoni on it from this place in the past. This led him to wonder what the average weight of a large cheese and pepperoni pizza was at Doug's Pizza Palace. Doug ordered a large cheese and pepperoni pizza from Doug's Pizza Palace on 15 randomly selected days during a particular term and weighed each before eating it. Suppose all conditions are met for inference using the one-sample t-methods. The student constructed a 95% confidence interval for the population mean using the one-sample t-methods. How many degrees of freedom does the t critical value have?
14
Can pleasant smells improve learning? Researchers timed 21 subjects as they tried to complete paper-and-pencil mazes. Each subject attempted a maze both with and without the presence of a floral aroma. Subjects were randomized with respect to whether they did the scented trial first or second. Suppose a paired t-test is to be performed to determine whether there is evidence to indicate that the time to complete the maze is faster in scented trials compared to unscented trials, on average. The summary statistics for the difference in time to complete the maze (in seconds) between the unscented and scented trials (unscentedminus−scented) are x overbarxequals=3.85 and sequals=13.01. How many degrees of freedom does the t-statistic have?
20
A random sample of 25 students in an Introductory Statistics course were asked how many hours of sleep they got last night. The average of these 25 students was 5.4 hours with a standard deviation of 1.3 hours. Suppose all conditions are met for inference using the one-sample t-methods. Calculate the upper bound of a 95% confidence interval for the mean number of hours students in the Introductory Statistics course slept last night.
5.9366 hours
A medical study was investigating if getting a flu shot actually reduced the risk of developing the flu. A hypothesis test is performed. Suppose the null hypothesis was rejected with a p-value of 0.0002. The power of the test was 0.90. What type of error could be made and what is the probability of making that error?
A Type I error could be made with a probability of 0.0002.
A confidence interval for a population mean __________.
A confidence interval for a population mean gives possible values the true population mean will be with a certain level of confidence.
A critical value is _____________.
A critical value is the number of standard errors (or standard deviations) to move from the mean of a sampling distribution to correspond to a specified level of confidence.
When should a paired t-test be performed instead of a two-sample t-test?
A paired t-test should be performed instead of a two-sample t-test when each observation in one group has a dependence on a particular observation in the other group.
When should a paired t-test be performed?
A paired t-test should be performed when the variable of interest is quantitative, there are two groups being compared, and the samples taken are dependent.
It is hypothesized that 50% of Americans attend church regularly. Which of the following would be an example of making a Type I Error?
A study was conducted that had evidence to reject the null hypothesis. In reality, half of Americans actually do attend church regularly.
A p-value is the probability _____________.
A p-value is the probability of observing the actual result, a sample mean, for example, or something more unusual just by chance if the null hypothesis is true.
Researchers conducted a study and obtained a p-value of 0.75. Based on this p-value, what conclusion should the researchers draw? Choose the correct answer below.
Fail to reject the null hypothesis but do not accept the null hypothesis as true either.
Alex hypothesized that, on average, students study less than the recommended two hours per credit hour each week outside of class. Which of the following is Alex's alternative hypothesis?
H1: μ < 2 hours per week per credit
Which of the following would increase the width of a confidence interval for a population mean?
Increase the level of confidence
A student wondered if more than 10% of students enrolled in an introductory Chemistry class dropped before the midterm. He noticed that 2 out of 15 of his friends in the class dropped before the midterm. Based on his sample, he performed a hypothesis test. Is the hypothesis test a one-tailed or two-tailed test?
It is a two-tailed test since the alternative hypothesis states that the parameter is not equal to the hypothesized value.
Jan performed a study and obtained a p-value of 1.24. What conclusion should Jan make?
She made an error since it is not possible to get a p-value of 1.24
Suppose overbar x = 60, H0: μx =50, HA: μx >50, and the p-value from a one-sample test is 0.04. What does this p-value mean?
The probability of getting a sample mean of 60 or more if the true population mean is 50 is 0.04.
Is the average body temperature of humans really 98.6degrees°F? After sampling 15,600 healthy people from around the country, researchers found a sample mean of 98.5degrees°F. The p-value was 0.0001. Which of the following is true?
The results are "statistically significant" because the sample size was quite large and the p-value was quite small.
Is the length of 3/4" screws different than 3/4", on average? A random sample of 3/4" screws produced the following 95% confidence interval for the mean length of 3/4" screws: (0.748,0.754) in inches. Which of the following is true?
There is not enough evidence at the 5% significance level to indicate the mean length of 3/4" screws is different than 3/4".
Researchers timed 21 subjects as they tried to complete paper-and-pencil mazes. Each subject attempted a maze both with and without the presence of a floral aroma. Subjects were randomized with respect to which trial they did first. Suppose a paired t-test is to be performed to determine whether there is evidence to indicate that the time to complete the maze is faster in scented trials compared to unscented trials, on average. The p-value from the paired t-test is 0.11. Which of the following is the most appropriate conclusion based on this p-value?
There is not sufficient evidence to indicate that the individuals complete mazes faster with a floral aroma present compared to when no floral aroma is present, on average.
Clifford likes dogs. He wondered how much dog owners spend on their dogs in a year. He hypothesized that dog owners spend more than $1000 a year on their dogs, on average. He sampled 75 dog owners in a local community and found that these 75 dog owners spent an average $1075 on their dogs in a year. Suppose sigma σx=$175. Assume that these 75 dog owners are representative of all dog owners in terms of amount spent on their dogs in a year. The p-value is 0.0001. What conclusion should be made?
There is strong evidence to reject the null hypothesis
A certain marathon has had a wheelchair division since 1977. An interested fan wondered who is faster: the men's marathon winner or the women's wheelchair marathon winner, on average. A paired t-test was performed, and the p-value was found to be 0.001. Which of the following is the correct conclusion?
There is sufficient evidence to indicate that the men's running winning time and the women's wheelchair winning time each year are different, on average.
Why does sample size need to be accounted for in the t-distribution?
The t-distribution changes for different sample sizes.
It is recommended that adults get 8 hours of sleep each night. A researcher hypothesized college students got less than the recommended number of hours of sleep each night, on average. The researcher randomly sampled 50 college students and calculated a sample mean of 7.9 hours per night. The researcher performed a hypothesis test. What is the null hypothesis?
Upper H0: μx = 8 hours per night
When is it appropriate to use the pooled two-sample t-methods?
Use the pooled two-sample t-methods when the samples come from different populations with the same, or nearly the same, standard deviations.
A graduate student wanted to estimate the average time spent studying among graduate students at her school. She randomly sampled graduate students from her school and obtained a 99% confidence interval of (17.3,22.5) hours/week. In the context of the problem, which of the following interpretations is correct?
We are 99% sure that the average amount of time spent studying among graduate students at this student's school is between 17.3 and 22.5 hours per week.
When are conclusions said to be "statistically significant"?
When the p-value is less than a given significance level
Cuckoos lay their eggs in the nests of other (host) birds. The eggs are then adopted and hatched by the host birds, but the potential host birds lay eggs of different sizes. A random sample of sparrow host eggs and wagtail host eggs was taken and the length of the cuckoo eggs for each host was recorded. Based on the sample data, suppose a 95% confidence interval for the difference in mean lengths of cuckoo eggs (sparrow hostsminus−wagtail hosts) is (minus−0.6,minus−0.1) mm. Is there evidence at the 5% significance level to indicate that cuckoos do change the size of their eggs between sparrow and wagtail hosts, on average?
Yes, since 0 is not between the lower and upper bounds of the confidence interval.
Elmo likes music. He wondered if listening to music while studying will improve scores on an exam. Fifty students who were to take the midterm in a week agreed to be part of a study. Half were randomly assigned to listen to classical music while studying for the exam. The other half were told not to listen to any music while studying for the exam. A hypothesis test is to be performed to determine if the average scores of those listening to music while studying for the exam were higher than those who did not listen to any music while studying for the exam. Which of the following hypothesis tests should be used?
a two-sample t-test
In 1993, the British Medical Journal published an article titled, "Is Friday the 13th Bad for Your Health?" Researchers in Britain examined how Friday the 13th affects human behavior. One question was whether people tend to stay at home more on Friday the 13th. The accompanying data give the number of cars passing Junctions 9 and 10 on the M25 motorway for consecutive Fridays (the 6th and 13th) for five different time periods. Assuming all conditions for inference are met, which test is appropriate to use to answer the researcher's question of interest?
paired t-test
A professor wondered if there was a difference in the proportion of students who dropped math classes between females and males. The professor randomly selected 20 math classes around campus and recorded the gender of the individual and whether or not a student enrolled in the class at the beginning of the term dropped the class at some point during the term. Assuming all conditions are satisfied, which of the following tests should the researcher use?
two-sample z-test for proportions