Question

You wish to test the following claim (H1H1) at a significance level of α=0.02α=0.02.

      H0:μ=82.7H0:μ=82.7
      H1:μ>82.7H1:μ>82.7

You believe the population is normally distributed, but you do not know the standard deviation. You obtain a sample of size n=28n=28 with mean ¯x=93.7x¯=93.7 and a standard deviation of s=20.8s=20.8.

When finding the critical value and test statistic, which distribution would we be using?

• Normal distribution (invNorm for critical value)
• T distribution (invT for critical value)
• χ2χ2 distribution (invχχ for critical value)
• F distribution (invF for critical value)

Answer 1

Solution :

= 82.7

= 93.7

S = 20.8

n = 28

This is the right tailed test .

The null and alternative hypothesis is ,

H0 :    = 82.7

Ha : > 82.7

T distribution using

Test statistic = t

= ( - ) / S / n

= (93.7- 82.7) / 20.8 / 28

= 2.798

Test statistic = t = 2.798

The information provided, the significance level is α=0.02, and the critical value for a right-tailed test is tc = 2.158

P-value =0.0047

= 0.02

P-value <

0.0047 < 0.02

Reject the null hypothesis .

There is sufficient evidence to suggest that