Question

The time to repair an electronic instrument is a normally distributed random variable measured in hours.
The repair time for 16 such instruments chosen at random are as follows:

Hours
159
224
222
149
280
379
362
260
101
179
168
485
212
264
250
170

(a) You wish to know if the mean repair time exceeds 225 hours. Set up appropriate hypotheses for investigating this issue.
(b) Test the hypotheses you formulated in part (a). What are your conclusions? Use α = 0.05.
(c) Find the P-value for this test.
(d) Construct a 95 percent confidence interval on mean repair time

Answer 1

Answer: (a) the hypotheses to be set up are: Null hypothesis = the mean repair time is equal to 225 hours and the Alternative hypothesis = the mean repair time exceeds 225 hours

(b) The conclusion is that the mean repair time does not exceed 225 hours

(c) p-value = 0.2571

(d) 95% confidence interval = 188.93, 294.07

Step-by-step explanation: please find the attached document below

Answer 2

Following are the solution to the given points:

For point a)

$H_0 :\mu =225\\\\H_1 :\mu >225$

For point b)

$\to \bar{y}=241.50\\\\ \to s^2=\frac{146202}{16-1}=9746.80\\\\\to S=\sqrt{9746.8}=98.73$

$\to t_0= \frac{\bar{y} - \mu_0} {\frac{S}{\sqrt{n}}}$  

       $=\frac{241.50-225}{\frac{98.73}{\sqrt{16}}} \\\\= 0.67$

Since   $t_{0.05,15 }$

don't reject $H_0$

For point c)

Please find the attached file.

$\to P=0.26$

For point d)

When $95\%$  CI is:

$\to \bar{y} -t_{\frac{\alpha}{2} \ n-1} \frac{S}{\sqrt{n}} \leq \mu \leq \bar{y} + t_{\frac{\alpha}{2} \ n-1} \frac{S}{\sqrt{n}}\\\\\to 241.50 - (2.131) \frac{98.73}{\sqrt{16}} \leq \mu \leq 241.50 + (2.131) \frac{98.73}{\sqrt{16}}\\\\\to 188.9 \leq \mu \leq 294.1$

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