Question

acme fears that 20% of its management trainees quit within one year of completing the training program. of the past 85 trainees, 14 have quit within 12 months. test the hypothese at alpha=.01 and determine which statements are true.

the sample proportion is 14%

the hypothesis should not be rejected because the lower boundary of the DNT region is bound to .09

the hypothesis should be rejected because the sample proportion falls into the rejection region.

please show work

Answer 1

We have give information for this question acme fears that population proportion is P = 20% of its management tranees quits within one year completing training out of 85 trainees.

P = 20% = 0.2, N=85 and sample size is (n)=14,

sample proportion is = 14/85 = 16.4%

So that the given statement sample proportion is 14% is not true.

Next hypothesis

H0: P= vs H1: P and alpha=0.01

Now to find the confidence interval for pupulation propotion P,

- Zc * square root(*(1-)) / n)) < P < + Zc * square root(*(1-)) / n)), where Zc is critical value

now we find zc=-6.62161 it is critical value at alpha=0.01

the confidannce interval for population proportion is  ( 0.09, 0.17).

So that the population propotion 0.20 is not lies between above confidance interval,

That is the give statment is ture, hypothesis should be rejected because the sample proprotion falls into the rejecton region.

Conclustion:

The sample proportion is 14% it is NOT TRUE.

The hypothesis should not be rejected because the lower boundary of the DNT region is bound to .09 it is NOT TRUE.

The hypothesis shuld be rejected because the sample proportion falls into the rejection region it is TRUE