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Each box of Healthy Crunch breakfast cereal contains a couponentitling you to a free package of garden seeds. At the HealthyCrunch home office, they use the weight of incoming mail todetermine how many of their employees are to be assigned tocollecting coupons and mailing out seed packages on a given day.(Healthy Crunch has a policy of answering all its mail on the dayit is received.) Let x = weight of incoming mail andy = number of employees required to process the mail inone working day. A random sample of 8 days gave the followingdata.

x (lb)	14	22	15	6	12	18	23	25
y (Number of employees)	7	10	9	5	8	14	13	16

In this setting we have Σx = 135, Σy = 82,Σx² = 2563, Σy² = 940, andΣxy = 1530.

(f) Find S_e. (Round your answer to threedecimal places.)
S_e =

(g) Find a 95% for the number of employees required to process mailfor 14 pounds of mail. (Round your answer to two decimalplaces.)

lower limit   Â	employees
upper limit   Â	employees

(h) Test the claim that the slope β of the populationleast-squares line is positive at the 1% level of significance.(Round your test statistic to three decimal places.)

t =

Find or estimate the P-value of the test statistic.

P-value > 0.250

0.125 < P-value < 0.250   

0.100 < P-value < 0.125

0.075 < P-value < 0.100

0.050 < P-value < 0.075

0.025 < P-value < 0.050

0.010 < P-value < 0.025

0.005 < P-value < 0.010

0.0005 < P-value < 0.005

P-value < 0.0005

Conclusion

Reject the null hypothesis, there is sufficient evidence thatβ > 0.

Reject the null hypothesis, there is insufficient evidence thatβ > 0.   

Fail to reject the null hypothesis, there is sufficient evidencethat β > 0.

Fail to reject the null hypothesis, there is insufficientevidence that β > 0.

(i) Find an 80% confidence interval for β and interpretits meaning. (Round your answers to three decimal places.)

lower limit   Â
upper limit   Â

Interpretation

For each less pound of mail, the number of employees neededincreases by an amount that falls within the confidenceinterval.

For each additional pound of mail, the number of employeesneeded increases by an amount that falls outside the confidenceinterval.    

For each additional pound of mail, the number of employeesneeded increases by an amount that falls within the confidenceinterval.

For each less pound of mail, the number of employees neededincreases by an amount that falls outside the confidenceinterval.