Question

Average college cost of tuition fee for all private institutions last year was P 36,400. A random sample of costs this year for 45 institutions of higher learning indicated that the sample mean was P 37,900 and sample standard deviation was P 5,600. At the 0.10 level of significance, is there sufficient evidence t0 conclude that the cost has increased?

Answer 1

$H_0:a=36400$

$H_1:a>36400$

Test statistic: $T={\frac {(x-a)*\sqrt n} {\sigma}}$ , where x - sample mean, a - assumed mean, n - sample size, $\sigma$ - standard deviation

in the given case we have: $T={\frac {(37900-36400)*\sqrt {45}} {5600}}=1.797$

Since sample size is big(>30), then it is appropriate to use z-score as critical value, so

$P(Z>Cr)=\alpha=0.1\implies Cr=1.282$

Since T>Cr, then we should reject the null hypothesis and conclude that, based on the obtained data, mean is significantly greater than 36400