Module 10 porblems IRead-Onlyl [Compasibility Model - Word ferences Mailings Rev

Question

Module 10 porblems IRead-Onlyl [Compasibility Model - Word ferences Mailings Review View Tell me what you want to do ·A-. = E.:a I'Normal!!No Spac. Heading 1 Heading 2 Title SubtitieSubtle En. Emphasis Module 10 SHOW ALL WORK FOR CREDITI if using calculator, show what function you used) l) A random sample of 250 college females showed that 76 use their cell phones during class even when prohibited. Construct a 95% confidence interval to describe the true proportion of females that use their cell phones during class even when prohibited and 2) A random sample of 23 teachers showed an average salary of 539,000. While the population standard deviation is unknown, the sample standard deviation is known to be $3,000. Construct a 99% confidence rterval to describe the true mean salary or teachers

Explanation / Answer

1) 95% Confidence interval : p+- z0.025 ((p(1-p)/n0.5)

where proportion of college females use cellphone during class, p = 76/250 = 0.304

95% CI = 0.304+-1.96((0.304)(0.696)/2500.5)

= (0.2778, 0.3302)

So 28% to 33% college femalesin the population use cell phones during class, we can say we are 95% confident that college females within the population use cell phones in proportion as mentioned in the above interval.

2) we will use t statistic confidence interval as poulation standard deviation is unknown and n<30

n = 23 and df = 23-1 =22

99% CI = sample mean +- t0.005,22(s/n0.5)

= 39,000+-2.819(3000/230.5)

= (37236.59 , 40763.41)

So the 99% true mean salary for the population is between the above mentioned range of interval

So we can say we are 99% confident that average salary of teachers in the whole population will fall within the above mentioned interval

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