Answer to Question #241522 in Statistics and Probability for mel

Question

The manufacturer of rechargeable electric shavers maintains that the mean working time of his product between charges is more than four hours. A random sample of fourteen shavers gives the following results (in minutes):

260

264

247

255

239

275

257

258

246

286

253

245

262

259

Test the manufacturer’s allegation at a 5% level of significance (assume normality).

Answer 1

SOLUTION

Form the hypothesis

Null Hypothesis $H_0:$ The mean working time of rechargeable electric havers is more than 4 hours

$H_0: \mu \gt4 hours$

Alternative Hypothesis, $H_a:$ The mean working time of rechargeable electric havers is less than 4 hours.

$H_a: \mu \lt4hours$

The $\alpha = 0.05$

I used Microsoft excel to run a hypothesis test on the data provided. I used T-test for hypothesized mean assuming equal variance.

The result of the hypothesis is in the picture below

Decision Making: The null hypothesis will be rejected if the p-value is less than the alpha = 0.05

The p-value = 0.0063930

The p-value = 0.0063930 is less than the alpha value = 0.05

Conclusion: Reject the null hypothesis, because the p-value is less than alpha value. There is no enough evidence to support the null hypothesis.