Question

Betsy is a survey researcher who knows from University records that the mean GPA of incoming students is 3.2 with a standard deviation of 0.3. She collects her own sample of 200 Memphis students and discovers that the mean incoming GPA in her sample is 3.5 and the standard deviation in her sample is 0.7.

Answer 1

Solution:-

95% confidence interval around the sample estimate is C.I = (3.458, 3.542).

$C.I = \bar{x}\pm z_{\alpha /2}\times \frac{S.D}{\sqrt{n}}$

C.I = 3.5 + 1.96 × 0.0212132

C.I = 3.5 + 0.041578

C.I = (3.458, 3.542)

Upper bound = 3.542

Lower bound = 3.458

Standard error of the mean is 0.0495.

$S.E= \frac{s}{\sqrt{n}}$

$S.E= \frac{0.70}{\sqrt{200}}$

S.E = 0.0495