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Math 1530
Terms in this set (19)
The null and alternative hypotheses are given. Determine whether the hypothesis test is left-tailed, right-tailed, or two-tailed and the parameter that is being tested
Ho : u = 9.4
H1 : u not equal to 9.4
two- tailed, u
The null and alternative hypotheses are given. Determine whether the hypothesis test is left-tailed, right-tailed, or two-tailed and the parameter that is being tested
Ho : o=8.8
H1 : o < 8.8
Left- tailed o
A_______ is a statement or claim regarding a characteristic of one or more populations.
Hypothesis
The ____ hypothesis contains the "=" sigh.
null
The mean monthly gasoline bill for one household is greater than
$130.
If a hypothesis test is performed, how should a decision that fails to reject the null hypothesis be interpreted?
There is no sufficient evidence to support claim u > $130
The mean number of rushing yards for a football team was less than
108
yards per game. If a hypothesis test is performed, how should a decision that rejects the null hypothesis be interpreted?
There is sufficient evidence to support the claim u < 108.
Test the hypothesis using the P-value approach. Be sure to verify the requirements of the test.
H0: p=0.4 versus H1: p>0.4
n=200; x=95; α= 0.05
Zo= 2.17
If P-value<α,
there is sufficient evidence to reject the null hypothesis at the given level of significance. If
P-value≥α,
there is insufficient evidence to reject the null hypothesis at the given level of significance.
In a study, researchers wanted to measure the effect of alcohol on the hippocampal region, the portion of the brain responsible for long-term memory storage, in adolescents. The researchers randomly selected 12
adolescents with alcohol use disorders to determine whether the hippocampal volumes in the alcoholic adolescents were less than the normal volume of
9.02cm3. An analysis of the sample data revealed that the hippocampal volume is approximately normal with no outliers and
x=8.12cm3 and s=0.7cm3.
Conduct the appropriate test at the α=0.01 level of significance.
State the null and alternative hypotheses.
H0 : μ =9.029.02
H1: μ <9.02
to =-4.45
P-value =0.000
The null hypothesis is REJECTED if the p-value is less than the level of significance. Otherwise, FAIL TO REJECT the null hypothesis.
A credit score is used by credit agencies (such as mortgage companies and banks) to assess the creditworthiness of individuals. Values range from 300 to 850, with a credit score over 700 considered to be a quality credit risk. According to a survey, the mean credit score is 704.2. A credit analyst wondered whether high-income individuals (incomes in excess of $100,000 per year) had higher credit scores. He obtained a random sample of
41 high-income individuals and found the sample mean credit score to be 724.2 with a standard deviation of 84.6.
Conduct the appropriate test to determine if high-income individuals have higher credit scores at the
α=0.05
level of significance.
H0:μ=704.2704.2
H1:μ than>704.2
Identify the to
to=1.51
P-value= 0.069
Make a conclusion regarding the hypothesis
FAIL TO REJECT the null hypothesis. There IS NOT sufficient evidence to claim that the mean credit score of high-income individuals is GREATER THAN 704.2.
What does it mean to say that two variables are positively associated? Negatively associated?
What does it mean to say that two variables are positively associated?
There is a linear relationship between the variables, and whenever the value of one variable increases, the value of the other variable increases.
What does it mean to say that two variables are negatively associated?
There is a linear relationship between the variables, and whenever the value of one variable increases, the value of the other variable decreases.
True or false: Correlation implies causation.
False
Match the linear correlation coefficient to the scatter diagram. The scales on the x- and y-axis are the same for each scatter diagram.
(a) r=−0.049,
(b) r=−0.969,
(c) r=-1
a. 2
b.1
c.3
An instructor wishes to determine if there is a relationship between the number of absences from his class and a student's final grade in the course. What is the explanatory variable?
Absences
A medical researcher wishes to determine if there is a relationship between the number of prescriptions written by pediatricians and the ages of the children for whom the prescriptions are written. She surveys all the pediatricians in a geographical region to collect her data. What is the response variable?
Number of prescriptions written
Compute the linear correlation coefficient between the two variables and determine whether a linear relation exists. Round to three decimal places.
r= 0.983; a linear relation exists
The data below are the number of absences and the final grades of 9 randomly selected students from a literature class. Find the equation of the regression line for the given data. What would be the predicted final grade if a student was absent 14 times? Round the predicted grade to the nearest whole number. Round the regression line values to the nearest hundredth.
D. y=−2.75x+96.14;58
A manager wishes to determine the relationship between the number of years her sales representatives have been employed by the firm and their amount of sales (in thousands of dollars) per month. Find the equation of the regression line for the given data. What would be the predicted sales if the sales representative was employed by the firm for 30 years? Is this reasonable? Why or why not? Round the predicted sales to the nearest dollar. Round the regression line values to the nearest hundredth.
A. y=3.53x+37.92;
$143,820; No, it is not reasonable. Thirty years of employment is well outside the scope of the model.
A county real estate appraiser wants to develop a statistical model to predict the appraised value of houses in a section of the county called East Meadow. One of the many variables thought to be an important predictor of appraised value is the number of rooms in the house. Consequently, the appraiser decided to fit the simple linear regression model,
y=β0+β1x, where y=appraised
value of the house (in $thousands) and x=number of rooms. Using data collected for a sample of n=74 houses in East Meadow, the accompanying results were obtained. Give a practical interpretation of the estimate of the slope of the least squares line.
D. For each additional room in the house, the appraised value is estimated to increase $22,740.
A county real estate appraiser wants to develop a statistical model to predict the appraised value of houses in a section of the county called East Meadow. One of the many variables thought to be an important predictor of appraised value is the number of rooms in the house. Consequently, the appraiser decided to fit the simple linear regression model, y=β0+β1x,
where y=appraised value of the house (in $thousands) and x=number of rooms. Using data collected for a sample of n=74 houses in East Meadow, the accompanying results were obtained. Give a practical interpretation of the estimate of the y-intercept of the least squares line.
B. There is no practical interpretation, since a house with 0 rooms is nonsensical.
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