Question

A new ACT preparation they recorded the are normally distributed.) claims that high school and practice ACT scores of 6 individuals after a one-month period. The results are shown in the following table: (Assume that ACT scores Test to see whether the preparation program will increase the ACT sco Sa is 1.2 in the tablel) e on avernagye by more than 0as points (Note thut the samolrnot the sle ) Alternatives Select one: O Mo 0.85 H, a 0.85 O None of the other four (i) Test statistic Select one: 〇!" " 2.015 2.571 3.365 5.883

Answer 1

(i)

Since this is a One-Tailed Test , we have :

Correct option :

$\dpi{100} H_0 : \mu_D \leq 0.85$

$\dpi{100} H_1 : \mu_D > 0.85$

(ii)

$\dpi{100} t = \frac{Sample\ mean - \mu_D}{\sqrt{S_D^2/n}}$

$\dpi{100} = \frac{2 - 0.85}{\sqrt{1.2/6}}$

$\dpi{100} = 2.571$

Correct option :

$\dpi{100} t^*= 2.571$

(iii)

P-value can be obtained by using Excel function :  TDIST(X, n - 1= degree of freedom , 1 = one tailed test )

$\dpi{100} Pvalue = TDIST(2.571,5,1) = 0.02497 \approx 0.025$

Correct option : Approximately 0.025

(iv)

Since P-value = 0.025 < 0.05 ( Level of significance) , we reject H_o and conclude that the preparation program will increase the ACT score by more than 0.85 points.

Correct option : Conclude H₁ that the preparation program will increase the ACT score by more than 0.85 points.