Question

2. A simple random sample of size n is drawn. The sample mean I is found to be 53.1, and the sample standard deviation s is found to be 7.8 a) (3 points) Construct a 95% confidence interval for the population mean u if the sample size n is 81. b) (3 points) Construct a 95% confidence interval for the population mean u if the sample size n is 30. c) (3 points) Construct a 90% confidence interval for the population mean y if the sample size n is 81. d) (1 points) From observing the answers to parts a) and b), what is the effect of decreasing the sample size on the width of the confidence interval? e) (1 points) From observing the answers to parts a) and c), what is the effect of decreasing the confidence % on the width of the confidence interval?

Answer 1

are -> Giren summary statistics x 53.1 and ase M at L20.05 Given that 281 The degrees of freedom difla 81-80 95% confidence interval for the population mean le (ñ a tale, af ( 1 ) ) > MG 58.11 tousle, 80 () (93.111.99009) ( 53.141.990069 X 0.866664 ) - Ma (53.1 t 1.12472133 ) =) (53.1-1.82472133, 53.1+1.72472193) -) HE (51.3452787, 54.8247213) 54.83.43 =) MG >> le (51.3753 leiren that 30 The de degrees freedom are dofanala 30-1229 95. confidence internal for population mean it le (ñ a tale, auf ( e )) at 220.05

=> le (53.1 I to.0572,28 -> (he) (534132 (830122.04523 X 10 42407865) 53.11 2.04523 x 7.8 5.47722558 al a e) (53.112.91256838) NG (530102091256838, 53.142.91256838) la (50.1874816 56.0125684) ! Ma cro. 1874 56.0126) ceiven that 7281 => dof=80 gon. confidence interval for population mean 2.0.1 Ca I t042, dof ()) at >> H+ (53.1470.61,80( 181 > RG (53.17 10664125 X 7. Toyo) (53.110664125% 0.866667) -> HA 053.4I 1.44224222 ) >> NE - (53.1-1.44224222,53.14 1644224222) 2) UE (51.6577578,54.5422422) dt (51.6576, 54.5422 )

@ from as the width of the confidence interval is width a upper limita lower limit width 54.8247 - 9.3753 width = 3.4494 from by the width of the confidence Internal is widan = 56.0126-50.1874 - 5.8252-☺ The widan of confidence internal increase as the sample size decreases from e) width of the confidence interval is width = 54.5422-51.6576 width = 2.8846 - © - from ☺re o we can say The width of confidence internal decreases as as the confidence J. decreases