Interpreting P-Values
When you are interpreting p-values, what is assumed to be true?
The null hypothesis.
A company that makes bungee cords has set a minimum breaking strength of 450Kg. If the mean breaking strength of sample drops below a specified level, the production is halted and machines are inspected. What would be a type 1 error?
Production is halted when the breaking strength is within specifications.
In an SRS of 120 US teenagers, the average number of texts received in a day is 57 with a standard deviation of 19. What is the 96% confidence interval for the average number of texts teens receive per day. The interval estimate must be in the form of statistic±crit・std.error.
57±2.08・ 19/sqrt120
A new diet is thought to increase weight more in lab mice than the current diet. New diet: n=10, mean increase in weight =4.8 oz, st. dev=0.3 oz. Current diet: n=10, mean=4 oz, st. dev=0.2 oz. What is the p-value?
p-value=0.00000608
What is the generic interpretation of a p-value?
Assuming the null is true, the probability of getting a sample statistic as extreme or more extreme is the p-value.
A company that makes bungee cords has set a minimum breaking strength of 450Kg. If the mean breaking strength of sample drops below a specified level, the production is halted and machines are inspected. What would be a type 2 error?
Production is not halted when breaking strength is below specifications.
An SRS of 35 city gas stations had a mean price of $3.45 per gallon for regular with a standard deviation of $0.05. Another SRS of 45 county gas stations had a mean of $3.25 per gallon with a standard deviation of 0.07. Construct a 95% confidence interval for the difference in means.
(0.1733,0.2267)
P=0.42, p-hat=0.37, Ha P<0.42, n=75
p-value =0.2064
Interpret the p-value.
If the true proportion is 0.42, the probability of getting a sample proportion of 0.37 for less is 0.2064
The county is thinking of cancelling school due to a approaching hurricane.
H0: The hurricane will not hit this area
What is a type 1 error?
School is cancelled and the hurricane did not hit this area.
We wish to know the life time of 2 major batteries. Suppose the standard deviation of each battery is 4.5 hours. How large of a sample (same for both batteries) should be taken if we wish to be 90% certain in the difference in battery life for these two batteries within 1 hour?
n≥110
x-bar=1060, s=55, n=200, Ha>1050, n=250
p-value=0.0022
Interpret the p-value.
If the true mean is 1050, the probability of getting a sample mean of 1060 or greater is 0.0022.
The county is thinking of cancelling school due to an approaching hurricane.
H0: The hurricane will not hit this area
What is a type 2 error?
School is not cancelled and the hurricane hit this area.
A confidence interval was constructed to estimate the mean GPA for all OCPS high school students. The 95% confidence interval estimate is 2.4±1.3. What is meant by "95 confidence"in context?
95% of all samples using the same collection method would result in an interval that captures the true mean GPA of all OCPS high school students.
How does doubling the sample size change the confidence interval size?
Divides the interval size by 1.414.