Question

1) (40) The life in hours of a battery is know ơ-3.5hours. A random sample of25 batteries hasa mean life off-25.5 hours. n to be approximately normally distributed, with historical standard deviation ' gnificance level or 10% (30) Can the manufacturer claim battery life exceeds 25 hours? Test with a si conclude using p-value. a. i. (10) Explain conclusion to people that do not know statisties FOR A-SHOW al steps from test Significance level Step K. 255 hours caloyledt on

Answer 1

(1)

Step 1:

H0: Null Hypothesis:

μ-25

HA: Alternative Hypothesis: (Claim)

μ>25

Step 2:
SE = $\sigma$/$\sqrt{n}$

= 3.5/$\sqrt{25}$ = 0.7

Step 3:

Test statistic is:

t = (25.5 - 25)/0.7 = 0.71

Step 4:

ndf = n - 1 = 25 - 1 = 24

One tail - Right Side

By Technology, P - Value = 0.2423

Step 5:

Since P - Value = 0.2423 is greater than $\alpha$ = 0.10, the difference is not significant. Fail to reject null hypothesis.

Step 6:

Conclusion:
The data do not support the manufacturer's claim that battery life exceeds 25 hours.

(2) Explain conclusion to people who do not know statistics:

Answer:

Though the sample mean = $\bar{x}$ = 25.5 > $\mu$ = 25, the increase of 0.5 is not significant and the increase is attributable to sampling variations only. So, we conclude:The data do not support the manufacturer's claim that battery life exceeds 25 hours