## Question 311:

Asked on August 4, 2008

Tags:
t-statistic ,
Null Hypothesis ,
Alternative Hypothesis ,
Z-Statistic ,
p-value

1

## Answer:

No answer provided yet.

**Null hypothesis** is that the mean pumpkin circumference is 39.9.
**Alternative hypothesis** is mean pumpkin circumference is NOT EQUAL to 39.9 so it is greater than or less than 39.9.
- For 100 pumpkins the sample is large enough that the z-test and t-test will be really close to each other, so the test-statistic will be the z-statistic or z-score which is calculated as the observed difference divided by the Standard Error of the Mean.
- The Standard Error of the Mean is calculated as the standard deviation divided by the square root of the sample size. In this case that is 1.6/SQRT(100) = 1.6/10 =.16.
- The
** test statistic** z is now (40.5-39.9)/.16 =** 3.75. **

- The p-value can be looked up by using the z-score to percentile calculator, enter 3.75 and 2-sided area. You should get a p-value of 0.0178% or .000178 to remove the percent sign.
- Since the p-value is far less than the previously stated significance level of .05 we'd reject the null hypothesis.
- We rejected the null hypothesis so we have good evidence that the claim that the mean pumpkin circumference is 39.9 is wrong. It is not off by a lot (only .6 cm) but it is not 39.9 (hopefully no one throws a pumpkin at us!).