Question

On average, a banana will last 7 days from the time it is purchased in the store to the time it is too rotten to eat. Is the mean time to spoil less if the banana is hung from the ceiling? The data show results of an experiment with 16 bananas that are hung from the ceiling. Assume that that distribution of the population is normal.

7.5, 7.6, 5, 6.5, 4.4, 8.2, 7, 4.4, 4.5, 5.3, 5.7, 6.4, 6.4, 7.8, 5.1, 6.4

What can be concluded at the the αα = 0.05 level of significance level of significance?

1. For this study, we should use Select an answer z-test for a population proportion t-test for a population mean
2. The null and alternative hypotheses would be:

H0:H0:  ? μ p  Select an answer < ≠ > =       

H1:H1:  ? μ p  Select an answer ≠ < = >    

3. The test statistic ? z t  =  (please show your answer to 3 decimal places.)
4. The p-value =  (Please show your answer to 4 decimal places.)
5. The p-value is ? ≤ >  αα
6. Based on this, we should Select an answer fail to reject reject accept  the null hypothesis.
7. Thus, the final conclusion is that ...
   • The data suggest the population mean is not significantly less than 7 at αα = 0.05, so there is statistically insignificant evidence to conclude that the population mean time that it takes for bananas to spoil if they are hung from the ceiling is equal to 7.
   • The data suggest that the population mean time that it takes for bananas to spoil if they are hung from the ceiling is not significantly less than 7 at αα = 0.05, so there is statistically insignificant evidence to conclude that the population mean time that it takes for bananas to spoil if they are hung from the ceiling is less than 7.
   • The data suggest the populaton mean is significantly less than 7 at αα = 0.05, so there is statistically significant evidence to conclude that the population mean time that it takes for bananas to spoil if they are hung from the ceiling is less than 7.

Answer 1

∑x = 98.2

∑x² = 626.78

n = 16

Mean , x̅ = Ʃx/n = 98.2/16 = 6.1375

Standard deviation, s = √[(Ʃx² - (Ʃx)²/n)/(n-1)] = √[(626.78-(98.2)²/16)/(16-1)] = 1.2670

a) Test used = t-test for a population mean

b) Null and Alternative hypothesis:

Ho : µ = 7 ;H1 : µ < 7

Test statistic:

t = (x̅- µ)/(s/√n) = (6.1375 - 7)/(1.267/√16) = -2.723

df = n-1 = 15

p-value = T.DIST(-2.7231, 15, 1) = 0.0079

Decision:

p-value < α, Reject the null hypothesis

Conclusion:

The data suggest the population mean is significantly less than 7 at α = 0.05, so there is statistically significant evidence to conclude that the population mean time that it takes for bananas to spoil if they are hung from the ceiling is less than 7.