AP Statistics
One Sample t-interval and t-test
A company has set a goal of developing a battery that lasts over 5 hours (300 minutes) in continuous use. In a first test of 12 of these batteries measured the following lifespans (in minutes): 321,295, 332, 351, 281, 336, 311, 253, 270, 326, 311, and 288. Is there evidence that the company has met its goal? Create an appropriate test.
Hypotheses:
Ho: µ = 300 The average lifespan of the batteries is 300 minutes.
HA: µ > 300 The average lifespan of the batteries is over 300 minutes.
Conditions:
1. Randomization: Not stated but we will assume a representative sample
2. 10% Condition: 12 batteries is less than 10% of all the batteries
3. Nearly Normal: The histogram is unimodal and approximately symmetric
All conditions have been met to use Student’s t-model for a one sample t-test.
Mechanics:
s = 29.31 α = 0.05
n = 12 d.f. = 11
Conclusion:
Since the P-Value is greater than alpha (0.238 > 0.05), I fail to reject the null hypothesis. There is not enough statistically significant evidence that the mean lifespan of the batteries is over 300 minutes.
Create a 98% confidence interval for the mean lifespan of this type of battery.
CI:
(283.25, 329.25)
I am 98% confident that the true mean lifespan of the batteries lies between 283.25 to 329.25 minutes.
Consumer Reports tested 14 brands of vanilla yogurt and found the following numbers of calories per serving:
160 200 220 230 120 180 140
130 170 190 80 120 100 170
· Create a 95% confidence interval for the average calorie content of vanilla yogurt.
Conditions:
1. Randomization: not stated but we will assume that it is a representative sample.
2. 10% Condition: 14 brands of yogurt is less than 10% of all brands of yogurt
3. NearlyNormal Condition:The Normal probability plot shows an approximate linear pattern
All conditions have been met to use Student’s t-model for a one sample t-interval
Mechanics:
CI:
(132.02,183.7)
I am 95% confident that the true mean of calories per serving lies between 132.02 and 183.7 calories.
· A diet guide claims that you will get 120 calories from a serving of vanilla yogurt. What does this evidence indicate? Use your confidence interval to test an appropriate hypothesis and state your conclusion.
Hypotheses:
Ho: µ = 120 The average calories per serving of vanilla yogurt is 120 calories.
HA: µ ≠ 120 The average calories per serving of vanilla yogurt is not 120 calories
Reject the claim because 120 is not in our interval.