Unit 6 Learning Content
An interested citizen wanted to know if Democratic U. S. senators are older than Republican U.S. senators, on average. On May 26 2013, the mean age of 30 randomly selected Republican Senators (sample 2) was 61 years 247 days old (61.675 years) with a standard deviation of 10.17 years. The mean age of 30 randomly selected Democratic senators (sample 1) was 61 years 257 days old (61.704 years) with a standard deviation of 9.55 years. What are the hypotheses for this study?
H0: µ1 = µ ; Ha: µ1 > µ2
Which of the following statements about hypotheses is false?
Hypothesis testing is used to prove the null hypothesis
Which of the following statements is NOT true:
In a one-tailed test, then the null hypothesis can be rejected based on either side
What is the last step of the parameter testing process
Reject the null, if possible
The results of a two sample mean test are shown below. What can be concluded?
The two means are significantly different
A bottle of water is labeled as containing 16 fluid ounces of water. You believe it is less than that. What type of test would you use?
left-tailed
Assume the p-value is 0.1243. Would you reject the null hypothesis?
no
If the p-value is 0.4955, what can be concluded about the research question?
the Democratic senators are not older than the Republican senators
If the alternate hypothesis is that the sample mean is greater than 10, the null hypothesis is
µ=10
If the confidence level is 95%, what is the alpha value in only one side of a two-tailed test?
2.5%
Which of the following statements is true?
A two-sided hypothesis has two tails and a two-sample test can have one or two tails
A null hypothesis that is 'equal to' a value has an expected range that is
Centered or to one side, depending on how it is worded.
A test that the sample mean is equal to a particular value will result in what kind of hypothesis test?
Either one or two-tailed, depending on the researcher.
The mean speeds of fastball pitches from two different baseball pitchers are to be compared. A sample of 14 fastball pitches is measured from each pitcher. The populations have normal distributions. The table below the result. Scouters believe that Rodriguez pitches a speedier fastball. The p-value for this test is .0071. If Wesley is u1 and Rodriguez is u2 then the correct hypotheses are:
H0: u1=u2; Ha: u2>u1
Choose the incorrect answer: Hypothesis Testing:
Tests claims about sample data
What does it mean when the null hypothesis is rejected?
The alternative hypothesis is accepted
If a hypothesis test results in an unusual result
The null can be rejected
Which statement is true about hypothesis testing:
population parameters are tested in hypotheses
Suppose a baker claims that his bread height is more than 15 cm, on average. Several of his customers do not believe him. To persuade his customers that he is right, the baker decides to do a hypothesis test. He bakes 10 loaves of bread. The mean height of the sample loaves is 17 cm. The baker knows from baking hundreds of loaves of bread that the standard deviation for the height is 0.5 cm. and the distribution of heights is normal. Write the hypotheses: The p-value for test the baker conducts is .000
reject the null hypothesis and accept the alternate
A null hypothesis can only be :
rejected or not rejected
Which hypothesis has the equals sign?
the null
What is the conclusion of the study?
the students scored more than an average of 65
True or False: hypothesis testing is concerned with the 5% of unusual events:
true
What type of test is this? H0: p = 50 Ha: p ≠ 50
two-tailed
Previously, an organization reported that teenagers spent 4.5 hours per week, on average, on the phone. The organization thinks that, currently, the mean is higher. Fifteen randomly chosen teenagers were asked how many hours per week they spend on the phone. The sample mean was 4.75 hours with a sample standard deviation of 2.0. The null and alternative hypotheses are:
Ho: μ = 4.5, Ha: μ > 4.5
Statistically different means:
Results are not due to chance
True/False: Hypothesis testing for two samples is identical to testing one sample
false
True/False: If the two samples are not statistically different the null hypothesis can be rejected
false
True/False: P values are not used in hypothesis testing.
false
True/False: Two sample mean tests allow researchers to compare quantitative data to nominal data.
false
Assume H0: μ = 9 and Ha: μ < 9. Is this a left-tailed, right-tailed, or two-tailed test?
left-tailed
H0: μ = 10, Ha: μ < 10; What type of test is that?
left-tailed
What type of test would be run based on these hypotheses? Ho: μ = 5, Ha: μ < 5
left-tailed
When writing a null hypothesis, researchers want to
make it into a math statement
All of the following are true except for:
the larger the p-value the more statistically significant the result.
All of the following statements about p-values are true except:
the null hypothesis is rejected when the p-value is large
Choose the correct statement:
the null is the only hypothesis that can contain the = sign.
True or False: Hypothesis testing looks for unusual results.
true
True or False: When a difference is statistically significant, it is unusual.
true
If a confidence level of 95% is used, the range of the expected value includes
95% of the distribution
True/False: The alternate can be proven
False
True/False: The null can be proven
False
What is a null hypothesis?
The hypothesis that can be rejected
Which of the following statements is false?
The larger the p-value, the more statistically significant the result
Which statement is true
The null can be rejected
Which hypotheses can be rejected?
null only
The rejection area for the alternate hypothesis: µ> 50 would be:
on the right
Researchers interviewed street prostitutes in Canada and the United States. The mean age of the 100 Canadian prostitutes upon entering prostitution was 18 with a standard deviation of six. The mean age of the 130 United States prostitutes upon entering prostitution was 20 with a standard deviation of eight. Is the mean age of entering prostitution in Canada lower than the mean age in the United States? What type of test is this:
one-tailed left tailed
Choose the true statement:
only the null can be rejected and only the alternative can be accepted
The mean speeds of fastball pitches from two different baseball pitchers are to be compared. A sample of 14 fastball pitches is measured from each pitcher. The populations have normal distributions. The table below the result. Scouters believe that Rodriguez pitches a speedier fastball. The p-value for this test is .0071. If the p-value of this test is .007, what would your conclusion be: Pitcher Sample Mean Speed of Pitches (mph) Population Standard Deviation Wesley 86 3 Rodriguez 91 7
reject the null and accept the alternate hypothesis: Rodriguez is the speedier pitcher
Which of the following is more statistically significant than the p-value of .04?
.002
What would be your p-value based on excel output for a two-tailed test? z-Test: Two Sample for Means Variable 1 Variable 2 Mean 22.12 22.76 Known Variance 3.68 4.7 Observations 50 50 Hypothesized Mean Difference 0 z -1.5633 P(Z<=z) one-tail 0.058991 z Critical one-tail 1.644854 P(Z<=z) two-tail 0.117982 z Critical two-tail 1.959964
0.118
If the confidence level is set at 90%, what is the alpha value in only one side of a two-tailed test?
5%
Rejected the null is the same as
Accepting the alternate
If testing for a mean value LESS THAN a value, at the 95% confidence level
Alpha is defined as 5% on the left
Would you reject or not reject the null hypothesis based on this output?
Do not reject null hypothesis
True or False: there are two types of alternative hypotheses:
False
Which of the following statements is true?
In a two-tailed test, alpha is split into two with half for each of the two tails of a normal distribution
When conducting a two sample mean test, a negative z-score
Indicates the second sample is greater than the first
A two sample mean test is conducted to see if the samples equal each other. Using the confidence interval below, can the researcher reject the null that they are equal? CI 95% (z score 1.96) upper 1.754, lower 0.246
No, because the confidence interval does not include zero
A company wants to show that their batteries (Sample 1) last as long as much more expensive ones (sample 2). After taking appropriately sized samples, the following results were obtained. Should the marketing department be allowed to say the batteries last as long? (The standard used is typically a 95% level of confidence.) z-score: -2.02p-value: .0215
No, the z score is negative and the likelihood of the being the same is less than 2.5%
True or False: there are two types of hypotheses
True
True/False: The alternate hypothesis is the math complement of the null
True
True or False: A null hypothesis can prove results:
false
Assume a p-value is 0.0935. Would we reject or not reject a null hypothesis at the 95% level?
not reject
The p-value of a hypothesis the test is 0.0013 . What would be our decision?
reject the null hypothesis and accept the alternate
Statistical significance refers to:
results that could not be due to chance
Assume H0: μ ≤ 6 and Ha: μ > 6. Is this a left-tailed, right-tailed, or two-tailed test?
right-tailed
Your friend claims that his mean golf score is 63. You want to show that it is higher than that. What type of test would you use?
right-tailed
The mean lasting time of two competing floor waxes is to be compared. Twenty floors are randomly assigned to test each wax. Both populations have a normal distributions. The data are recorded in The table below. The p-value of our test is p-value = 0.1799. Wax Sample Mean Number of Months Floor Wax Lasts Population Standard Deviation 1 3 0.33 2 2.9 0.36 What can we conclude?
the lasting time of both waxes is not significantly different
A student at a four-year college claims that mean enrollment at four-year colleges is higher than at two-year colleges in the United States. Two surveys are conducted. Of the 35 two-year colleges surveyed, the mean enrollment was 5,068 with a standard deviation of 4,777. Of the 35 four-year colleges surveyed, the mean enrollment was 5,466 with a standard deviation of 8,191. If the p-value from the study is 0.4019 what is our conclusion?
the mean enrollment at four-year colleges is not higher than at two-year college
True or False: a null hypothesis is rejected when the p-value is low
true
True or False: a statistically significant result might not be an important result
true
Assume the null hypothesis states that the mean is equal to 88. The alternative hypothesis states that the mean is not equal to 88. Is this a left-tailed, right-tailed, or two-tailed test
two-tailed
A study was conducted to determine whether cell phone users developed brain cancer at a greater rate than non-cell phone users. In a study of 420,019 cell phone users, 172 of the subjects developed brain cancer. (the rate of brain cancer for non-cell phone users is 0.0340%). The results of this test were a p-value of .0073. Would the results above be important?
yes
A study was conducted to determine whether cell phone users developed brain cancer at a greater rate than non-cell phone users. In a study of 420,019 cell phone users, 172 of the subjects developed brain cancer. (the rate of brain cancer for non-cell phone users is 0.0340%). The results of this test were a p-value of .0073. Would these results be significant at the .05 level?
yes
Would a 10 point difference in your statistics score likely be significant?
yes
Suppose a statistics instructor believes that there is no significant difference between the mean class scores of statistics day students on Exam 2 and statistics night students on Exam 2. She takes random samples from each of the populations. The mean and standard deviation for 35 statistics day students were 75.86 and 16.91, respectively. The mean and standard deviation for 37 statistics night students were 75.41 and 19.73. The "day" subscript refers to the statistics day students. The "night" subscript refers to the statistics night students. An appropriate alternative hypothesis for the hypothesis test is:
μday ≠ μnight
What is a Hypothesis?
A testable statement about a population or sample
Write the null and alternate hypotheses: The mean number of years Americans work before retiring is less than 34.
H0: μ = 34; Ha: μ < 34
Suppose a baker claims that his bread height is more than 15 cm, on average. Several of his customers do not believe him. To persuade his customers that he is right, the baker decides to do a hypothesis test. He bakes 10 loaves of bread. The mean height of the sample loaves is 17 cm. The baker knows from baking hundreds of loaves of bread that the standard deviation for the height is 0.5 cm. and the distribution of heights is normal. Write the hypotheses:
H0: μ = 15 The alternate hypothesis is Ha: μ > 15
A college football coach records the mean weight that his players can bench press as 275 pounds, with a standard deviation of 55 pounds. Three of his players thought that the mean weight was more than that amount. They asked 30 of their teammates for their estimated maximum lift on the bench press exercise. What are the hypotheses for this test?
H0: μ = 275 ; Ha: μ > 275
Statistics students believe that the mean score on the first statistics test is 65. A statistics instructor thinks the mean score is higher than 65. He samples ten statistics students and obtains the scores 65; 65; 70; 67; 66; 63; 63; 68; 72; 71. He performs a hypothesis test using a 5% level of significance. The data are assumed to be from a normal distribution. What are the hypotheses for this test?
Ho: μ = 65, Ha: μ > 65
Statistical Significance refers to all but:
Importance of a result
What can you conclude if the results of a one-sample test include the following information? The z-score is 1.56 and the p-value is .0576.
The results are not statistically significant
Would a one-point difference in your statistics score likely be significant?
no
What type of test is it if the alternative hypothesis is written with an equal sign?
none of these can be used
Statistics students believe that the mean score on the first statistics test is 65. A statistics instructor thinks the mean score is higher than 65. He samples ten statistics students and obtains the scores 65; 65; 70; 67; 66; 63; 63; 68; 72; 71. He performs a hypothesis test using a 5% level of significance. The data are assumed to be from a normal distribution. If the p-value is 0.0396 , would you reject or not reject the null hypothesis?
reject
H0: μ = 1, Ha: μ > 1; what type of test is this?
right-tailed
True or False: in a two-tailed hypothesis test, alpha is split into two tails of the normal distribution so unusual can occur in either tail.
true
True/False: Testing a sample mean requires knowing the size of the sample
true
When a researcher is not sure about the direction of an outcome, they would use which type of alternate hypothesis?
two-tailed
If the alternate hypothesis is written with a ≠ sign, it is what type of test?
two-tailed test
What statement is not true about the null hypothesis
when we reject a null, we have proven it
Researchers interviewed street prostitutes in Canada and the United States. The mean age of the 100 Canadian prostitutes upon entering prostitution was 18 with a standard deviation of six. The mean age of the 130 United States prostitutes upon entering prostitution was 20 with a standard deviation of eight. Is the mean age of entering prostitution in Canada lower than the mean age in the United States? With a p-value of .0151 is the difference significant at the .05 level?
yes