Question

survey used to collect data on incerview of a randomly-selected sample of aduits. One of the questions on the survey is an average work dey, about how many hours do you have to relex or prve ototes that Tpu epy? A95% co farce ineervai from the 2010 GSS srvey is 353 to 383 hours. a) Which of the following is a vaid ü 95% of Americans relax or pursue enjoyable activities between 3 99% af Americans in this umple relax or pursue ergoystie a activities bebeeen 353 and 3.83 hours on an average workday activides between 3.53 and 3.83 hours on an average workday Of this survey "enresult i", interval that captures the true population mean 95% of Assume the Larger or puruuing enjoyable activities on an average warkday?e your answer to two decimal places d)awlenge, Fnd the 99% corndence r terv.1 for rumber of Give your endpoints to 9% confidence int n hours: 6 0 3 Q W E RTYU0 P tab

Answer 1

a) since the sample represents the population the 95% confidence interval represents as follows

95% of the americans relax or pursue enjoyable activities between 3.53 to 3.83 hours on an average working day.

b) If we consider 90% confidence interval the interval will become shorter because the critical value for 90% confidence is lesser than 95% confidence.

c) Mean = (3.83+3.53)/2 = 3.68 hours

d) Keeping all other things constant only changing the confidence interval

for 95% Confidence margin of Error = 0.15 hours

E = $Z_{\alpha/2}*\sigma/\sqrt{n}$

$\sigma/\sqrt{n} = \frac{0.15}{1.96}$ = 0.0765

99% CI E = 0.0765*2.58 = 0.197

99% CI = (3.68 - 0.197 , 3.68+0.197) = ( 3.483, 3.877)