z-values and t-values
Confidence Intervals
p-value approach
critical value approach
linear regression and correlation
100
The critical z-value for a left-tailed hypothesis test performed at a 5% level of significance rounded to two decimal places
What is -1.64 ?
for a left tail test, alpha = 0.05 is area in left tail
so z = invNorm(0.05, 0, 1)
100
The 98% confidence interval for the average number of absences for a MATH class is (3.77, 4.23).
The margin of error for this confidence interval is
What is 0.23 ?
given confidence interval (lower bound, upper bound), the margin of error = (upper bound - lower bound) / 2
100
To find p-values in hypothesis testing, you would use this function in your calculator
What is normalcdf( ?
100
For hypothesis testing,
To find critical z-values, rounded to two decimal places, you would use this function in your calculator
and
to find critical t-values, rounded to three decimal places, you would use this function in your calculator
What are invNorm( and invT( ?
100
The value of the correlation coefficient is -0.784
The relationship between x and y can be described as ___________ and __________ .
A scatter plot with this correlation coefficient would have points that _______ from left to right.
What are strong, negative, and fall ?
200
The t-value for a sample size of 18 and 98% confidence level rounded to three decimal places
What is 2.567 ?
n = 18 so df = 18 - 1= 17
c = 0.98 so area right = (1-0.98)/2 = 0.01
t = invT(1-0.01, 17)
200
For a population data set, σ = 12.5,
find the sample size that should be selected so that the margin of error of estimate for a 96% confidence interval for μ is 3.20.
Round up to the nearest whole number.
What is 65 ?
use formula to find n with σ = 12.5, ME = 3.20, and c = 0.96
Note: you will use invNorm(0.96, CENTER, 0, 1) or invNorm(1-0.02, 0, 1) to find z
200
For a two-tailed hypothesis test with an observed z-value of -2.98, the p-value, rounded to four decimal places, would be
What is 0.0029 ?
for two-tailed hypothesis test and a negative observed z,
p = 2 x normalcdf(-E99, -2.98, 0, 1)
200
For a left - tailed hypothesis test performed at a 3% level of significance with sample size of 17, the critical t-value, rounded to three decimal places, is __________ .
What is -2.024 ?
for left-tail test, alpha is area in left tail
n = 17 so df = 17-1 = 16
t = invT(0.03, 16)
200
The regression equation of the line of best fit for the data below with a and b rounded to three decimal places.
What is y = 4.167 + 0.167 x ?
enter data as two lists into calculator and run STAT> CALC > 8:LinReg(a+bx) to get values of a and b and plug into equation form
300
The t-value with an area of 0.001 to its right and 23 degrees of freedom rounded to three decimal places
What is 3.485 ?
area right = 0.001 and df = 23
t = invT(1 - 0.001, 23)
300
A company that produces detergents wants to estimate the mean amount of detergent in 64-ounce jugs at a 99% confidence level. The company knows that the standard deviation of the amounts of detergent in all such jugs is 0.20 ounce.
Find the sample size the company should select so that the estimate is within 0.04 ounce of the population mean, rounded up to the nearest whole number.
What is 167 ?
use formula to find n with σ = 0.20, ME = 0.04, and c = 0.99
Note: you will use invNorm(0.99, CENTER, 0, 1) or invNorm(1-0.005, 0, 1) to find z
300
Consider H0 : μ = 72 versus H1 : μ > 72
A random sample of 16 observations taken from this population produced a sample mean of 75.2. The population is normally distributed with σ = 6.
The p-value, rounded to four decimal places, is __________ .
You would _________ the null hypothesis if the test were made at a significance level of 0.01.
What are 0.0166 and not reject ?
for right tailed test, p = normalcdf(obs z, E99, 0, 1)
and do not reject H0 bc p > alpha
300
For a right - tailed hypothesis test performed at a 1% level of significance, the critical z-value, rounded to two decimal places, is ____________ .
What is 2.33 ?
for a right tail test, alpha = 0.01 is area in the right tail
so z = invNorm(0.01, RIGHT, 0,1)
or z = invNorm(1-0.01, 0, 1)
300
The correlation coefficient for the data in the 200 point clue rounded to three decimal places
and
two words to describe the correlation
What are r = 0.183, positive, and weak ?
enter data as two lists into calculator and run STAT> CALC > 8:LinReg(a+bx) to get value of r
describe the correlation based upon whether r is positive or negative and how close r is to -1 or 1
400
The z-value for a 96% confidence interval rounded to two decimal places
What is 2.05 ?
c = 0.96 so area in CENTER = 0.96 or
area right = (1-0.96)/2 = 0.02
z = invNorm(0.96, CENTER, 0, 1)
or
z = invNorm(1-0.02, 0, 1)
400
A random sample of 65 employees selected from financial companies in New York City showed that they received an average bonus of $55,000 last year. The standard deviation of bonuses of all employees is $18,000.
Fill in the blank:
One can be 95% confident that the average bonus of all employees working for financial companies in New York City last year was between __________ and _____________ dollars.
What are 50624 and 59376?
given n = 65, x bar = 55000, σ = 18000, c = 0.95 use STAT>TESTS>7: ZInterval to find confidence interval
400
The manufacturer of a certain brand of auto batteries claims that the mean life of these batteries is 45 months. A consumer protection agency that wants to check this claim took a random sample of 24 such batteries and found that the mean life for this sample is 43.05 months. The lives of all such batteries have an approximate normal distribution with the population standard deviation of 4.5 months.
The p-value for the test of hypothesis with the alternative hypothesis that the mean life of these batteries is less than 45 months, rounded to four decimal places, is ___________.
You would _________ the null hypothesis at α = 0.025.
What are 0.0170 and reject ?
for left tail test, p = normalcdf(-E99, obs z, 0, 1)
reject H0 because p <= alpha
400
Consider H0 : μ = 80 versus H1 : μ ≠ 80 for a population that is normally distributed.
A random sample of 25 observations taken from this population produced a sample mean of 77 and a standard deviation of 8. Using α = 0.01, the null hypothesis would _________.
What is not be rejected ?
two tail test so rejection region would be in the two-tails
alpha =0.01/2 = 0.005 is area in each tail
so left t = invT(0.005, 25 - 1) = -2.797 and right t = + 2.797
obs t = -1.875 does not fall in rejection region
400
The value of the coefficient of determination for the data set in the 200 point clue rounded to three decimal places
What is 0.033 ?
enter data as two lists into calculator and run STAT> CALC > 8:LinReg(a+bx) to get value of r 2
500
The critical left and right t-values for a two-tailed hypothesis test with a 10% level of significance for a sample of size 20 rounded to three decimal places
What are -1.729 and +1.729 ?
alpha = 0.10 but for two-tail test, divide by 2
0.10/2 = 0.05 is area in right tail and area in left tail
n = 20 so df = 20-1 = 19
left t = invT(0.05, 19) = -1.729
right t = + 1.729
500
A random sample of 36 mid-sized cars tested for fuel consumption gave a mean of 26.4 miles per gallon with a standard deviation of 2.3 miles per gallon.
Use your calculator to find the 99% confidence interval for the population mean, μ. Round numbers to two decimal places.
What is (25.36, 27.44) ?
given n = 36, x bar = 26.4, s = 2.3, c = 0.99, use STAT>TESTS>8: TInterval to find confidence interval
500
According to a MyBankTracker study, the average checking account fee at top U.S. banks was $9.60 per month in 2018. A bank consultant wants to determine whether the current average checking account fee at top U.S. banks is more than $9.60 per month.
A recent random sample of 150 such checking accounts taken from top U.S. banks produced a mean checking account fee of $10.12 per month. Assume that the standard deviation of all such checking account fees at top U.S. banks is $3.12.
The p-value for this test of hypothesis, rounded to four decimal places, is ____________.
Based on this p-value, you would _______ the null hypothesis if the level of significance is 0.05.
What are 0.0207 and reject ?
for right tailed test, p = normalcdf(obs z, E99, 0, 1)
and reject H0 bc p <= alpha
500
According to a MyBankTracker study, the average checking account fee at top U.S. banks was $9.60 per month in 2018. A bank consultant wants to determine whether the current average checking account fee at top U.S. banks is more than $9.60 per month. A recent random sample of 150 such checking accounts taken from top U.S. banks produced a mean checking account fee of $10.12 per month. Assume that the standard deviation of all such checking account fees at top U.S. banks is $3.12. Perform a hypothesis test at the 1% level of significance.
The rejection region for this test would be in the ______ tail.
The critical z-value, rounded to two decimal places, is __________ .
The observed z-value, rounded to two decimal places, is ____________ .
We would ________ H0.
What are right, 2.33, 2.04, and not reject ?
for right tail test, alpha =0.01 is area in rejection region in right tail
so critical z = invNorm(0.01, RIGHT, 0, 1) or invNorm(1-0.01, 0, 1)
obs z = 2.04 does not fall in rejection region
500
The value of y rounded to the nearest whole number if x is 2 using the linear regression equation for the line of best fit from the 200 point clue
What is 5 ?
Using linear regression equation from 200 point clue, substitute 2 for x to get answer for y