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Confidence Interval and Hypothesis Testing
Of One Sample Mean Worksheet

MTH 160: Statistics
Read the following scenario and complete each of the problems below:
A flashlight company claims that the new bulb in its heavy duty flashlight will average 246 hours of light. A statistics student decides that he/she wants to test this claim at a 5% level of significance to determine if there is evidence to support the claim. The student randomly selects and tests 15 flashlight bulbs and records how long the bulb lasts until it burns out. Assume the life of a bulb is normally distributed. The data is in the table below:
Trial
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
Hrs:
246
224
231
242
237
240
243
236
239
255
256
239
247
231
253

A. Based on a histogram or box-plot of the data, what is the shape of the distribution (normal, skewed left, skewed right, uniform, etc.)? Explain why you can conduct a hypothesis test on the given data.

B. Evaluate the claim based on the following assumption: The standard deviation of the population is 7.4 hours.
1. Identify the type of test you will use to test the claim that the flashlight will average 246 hours of light. Explain your reasoning.
2. State the null and alternate hypotheses.
3. Conduct the hypothesis test and determine the p-value.
4. State your conclusion about the claim that the flashlight will average 246 hours of light.

5. Construct a 95% confidence interval for this study.
1.
2.
3.
4.
5.

C. Evaluate the claim based on the following assumption: The population’s standard deviation is not known.
1. Identify the type of test you will use to test the claim that the flashlight will average 246 hours of light. Explain your reasoning.
2. State the null and alternate hypotheses.
3. Conduct the hypothesis test and determine the p-value.
4. State your conclusion about the claim that the flashlight will average 246 hours of light.
5. Construct a 95% confidence interval for this study.
1.
2.
3.
4.
5.

D. Write a 200- to 400- word statement comparing and contrasting the two hypothesis test procedures and results.

Version 1
09/13
Version 1
7/1/13

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