Question

* Please notice that one of the answer is incorrect

5/ 10 pts Partial Question 3 A random sample of 22 fifth grade pupils have a grade point average as follows: 5, 5.5,4.5, 5, 5.5, 5, 5.5, 4.5, 5.5, 5, 5,4, 5.5, 4.5, 4.5, 5, 4.0, 6.0, 5.0, 5.5,4.5, 5.0. whereas marks range from 1 (worst) to 6 (excellent). The grade point average (GPA) of all fifth-grade pupils of the last five years is 4.7. Is the GPA of the 22 pupils different from the populations' GPA? Fill the values in the blanks. Reject the null hypothesis at significance level 0.05 if 〉 4.9319 | or if 〈 4.4681 Hint: keep exact 4 figures after the decimal point. Answer 1: 4.9319 Answer 2: 4.4681

Answer 1

$\dpi{100} \bar x$ = 4.977

s = 0.523

At alpha = 0.05, the critical values are t_{0.025, 21} = +/- 2.080

Reject H₀, if t < -2.08 or, t > 2.08

t < -2.08

or, ($\dpi{100} \bar x - \mu$)/(s/$\dpi{100} \sqrt n$) < -2.08

or, ($\dpi{100} \bar x$ - 4.7)/(0.523/$\dpi{100} \sqrt 22$) < -2.08

or, $\dpi{100} \bar x$ < -2.08 * (0.523/$\dpi{100} \sqrt 22$) + 4.7

or, $\dpi{100} \bar x$ < 4.4681

t > 2.08

or, ($\dpi{100} \bar x - \mu$)/(s/$\dpi{100} \sqrt n$) > 2.08

or, ($\dpi{100} \bar x$ - 4.7)/(0.523/$\dpi{100} \sqrt 22$) > 2.08

or, $\dpi{100} \bar x$ > 2.08 * (0.523/$\dpi{100} \sqrt 22$) + 4.7

or, $\dpi{100} \bar x$ > 4.9319

Reject the null hypothesis at significance level 0.05 if $\dpi{100} \bar x$ > 4.9319 or if $\dpi{100} \bar x$ < 4.4681.