1. State hypotheses by filling in the symbol (=,<,>, or not equal) and the popul

Question

1. State hypotheses by filling in the symbol (=,<,>, or not equal) and the population mean and determine if one or two tail:

2. Find critical z values with table F (which is below) is:

3. T test value is (round to three decimal places):

4. Reject the null or do not reject the null:

5. Conclusion: is or is not enough evidence.

An obstacle course was set up on a campus, and 11 volunteers were given a chance to complete it while they were being timed. They then sampled a new energy drink and were given the opportunity to run the course again. The "before" and "after" times in seconds are shown below. Is there sufficient evidence at = 0.05 to conclude that the students did better the second time? Assume the variables are normally distributed. Studen 1 2 3 4 5 6 7 89 10 11 Before70 78 82 75 69 68 76 81 77 67 72 After 65 75 78 68 65 70 73 76 73 68 70 Part 1 State the hypotheses and identify the claim with the correct hypothesis. 0: D- not claim claim This hypothesis test is a one-tailed test Part 2 out of 5 Find the critical value(s). Round the answer to three decimal places.

Explanation / Answer

The statistical software output for this problem is:

Paired T hypothesis test:
D = 1 - 2 : Mean of the difference between Before and After
H0 : D = 0
HA : D > 0
Hypothesis test results:

Hence,

Part - 2: From the table,

Critical value = 1.812

Part - 3: Test statistic = 3.905

Part - 4: Reject the null

Part - 5: is enough evidence

Difference Mean Std. Err. DF T-Stat P-value Before - After 3.0909091 0.79148359 10 3.9052093 0.0015

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