Number: "N=51".
Sum: "\\sum=1532"
"\\sum(x_i-\\bar{x})^2=3485.9215686275"
"Variance=s^2={\\sum(x_i-\\bar{x})^2 \\over N-1}={3485.9215686275 \\over 51-1}\\approx"
"\\approx69.718431372549"
"standard \\ deviation=s=\\sqrt{Variance}\\approx"
"\\approx\\sqrt{69.718431372549}\\approx8.35"
"H_0:\\mu=35"
"H_1:\\mu<35"
Left-tail test
The critical value (cutoff point) is "|z|=1.2816" In left-tail hypothesis testing, any z score less than the critical value will be rejected.
Since "-4.2763" is less than "-1.2816," we reject the null hypothesis. We accept the alternative hypothesis.
Yes, the training program has had the desired effect.
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