A cheerleading squad received a mean rating (out of 100 possible points) of 71 ±

Question

A cheerleading squad received a mean rating (out of 100 possible points) of

71 ± 9 ( ± )

in competitions over the previous three seasons. The same cheerleading squad performed in 16 local competitions this season with a mean rating equal to 73 in competitions. Suppose we conduct a one-independent sample z-test to determine whether mean ratings increased this season (compared to the previous three seasons) at a 0.05 level of significance.

(a) State the value of the test statistic. (Round your answer to two decimal places.)
z =

State whether to retain or reject the null hypothesis.

(b) Compute effect size using Cohen's d. (Round your answer to two decimal places.)
d =

Explanation / Answer

a)
Hypothesis:

Null hypothesis : mu = 71
alternative hypothesisL mu > = 71

Test statistuc :

z = ( x - mean)/( s/sqrt(n))
= ( 73 - 71) / ( 9/sqrt(16))
= 0.889

we need to find pvalue using z = 0.889 at 0.05 significance level.

P value = 0.1870

As p value is greater than significance level so, we fail to reject the null hypothesis.

b) Cohen's d = ( x - mean) / ( s/sqrt(n))
= ( 73 - 71) / ( 9/sqrt(16))
= 0.89
  

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