Question

A local greenhouse sells coffee-tree saplings. They price their saplings based on the height of the plant. They have two workers, Susan and Karen, who measure the saplings for pricing. The greenhouse manager wants to determine if there is a significant difference in the measurements made by these two individuals. She has them measure the same set of 15 saplings. Assume that the differences are calculated as Susan – Karen.

a) Select all of the correct null and alternative hypotheses.

Select one or more:

H₀: μd=0

H₀: μd=15

H₀: μd≠15

H₀: μd≠0

H_A: μd≠0

H_A: μd≠15

H_A: μd<15

H_A: μd>15

b) Use the data to compute the test statistic for the difference between Susan and Karen. For help using StatCrunch for a Paired Difference T-Test click here. Give your answer to four decimal places.

(The test statistic was compute using the data and these were the results)

Options Paired T hypothesis test: Up = uj - U2 : Mean of the difference between Susan and Karen Ho : UD = 0 HA: UD = 0 Hypothesis test results: Difference Mean Std. Err. DF T-Stat P-value Susan - Karen -0.27825333 0.14349385 14 -1.9391308 0.0729 Differences stored in column, Differences.

c) From this hypothesis test, choose the correct conclusions.

Select one or more:

We reject the null hypothesis.

We fail to reject the null hypothesis.

We conclude that there is a significant statistical difference between the two employees' measurements.

We conclude that there is not a significant statistical difference between the two employees' measurements.

On average in the sample, Susan has larger values than Karen.

On average in the sample, Karen has larger values than Susan.

We can not tell whether Susan or Karen has larger values on average.

Answer 1

Answer :

The greenhouse manager wants to determine if there is a significant difference in the measurements made by these two individuals.

n=sample size=15

Assuming that the differences are calculated as Susan – Karen.

a)

Therefore, null and alternative hypotheses is,

H0: μd=0 Vs. HA: μd≠0

b)

From the given out put,

T Stat= -1.9391

P-Value=0.0729 > $\alpha$ = 0.05

C)

Decision: We accept H0.

That is, We fail to reject the null hypothesis.

We conclude that there is not a significant statistical difference between the two employees' measurements.