## Question 311:

1

1. Null hypothesis is that the mean pumpkin circumference is 39.9.
2. Alternative hypothesis is mean pumpkin circumference is NOT EQUAL to 39.9  so it is greater than or less than 39.9.
3. 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.
1. 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.
2. The test statistic z is now (40.5-39.9)/.16 = 3.75.
4. 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.
5. Since the p-value is far less than the previously stated significance level of .05 we'd reject the null hypothesis.
6. 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!).