Light bulbs of a certain type are advertised as having an average lifetime of 75

Question

Light bulbs of a certain type are advertised as having an average lifetime of 750 hours. The price of these bulbs is very favorable, so a potential customer has decided to go ahead with a purchase agreement unless it can be conclusively demonstrated that the true average lifetime is smaller than advertised. A random sample of 50 bulbs was selected, the lifetime of each bulb determined, and the appropriate hypotheses were tested using a statistical software program, resulting in the following output: n - 50 738.44 s 38.20 (a) Write down the appropriate hypotheses and compare with your group. (b) The test statistic is closest to: -2.14 (c) The p-value for the test is closest to: 0.016 (d) At significance level.01, what is your conclusion? Fail to reject the null hypothesis; don't buy the bulbs.

Explanation / Answer

a)
Null and alternate hypothesis
H0: mu >= 750
Ha: mu < 750

b)
Test statistic,
z = (738.44 - 750)/(38.2/sqrt(50)) = -2.14

c)
p-value = 0.016 .. using standard z-table

d)
As p-value is greater than the significance level of 0.01, we fail to reject the null hypothesis.

This means that there are not significant evidence to conclude that mean life is less than 750.

Related Questions

Navigate

• Browse (All)
• Browse L
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.