Question

According to the popular idea when we look at the moon on the horizon, the latter seems larger than when we observe it at the zenith. You have decided to verify this statement. You asked participants how wide the moon should be at its zenith to be the same size as the horizon. You have obtained the following descriptive ratios and statistics:

x = size zenith/size horizon

x = {1.23, 1.06, 1.03, 1.4, 0.95, 1.13, 1.41, 1.23, 1.63, 1.56}

Mean = 1.26

Standard deviation = 0.23

Using a critical threshold of 5%, is the popular idea verified or not?

Answer 1

Answer:

Given,

Mean = 1.263

Standard deviation = 0.23

significance level = 0.05

Sample n = 10

degree of freedom = n - 1

= 10 - 1

= 9

t(alpha/2,df) = t(0.025,9) = 2.26

test statistic z = (x-u)/(s/sqrt(n))

substitute values

= (1.263-0)/(0.23/sqrt(10))

= 17.365

Here we observe that, test statistic > critical value, so we reject null hypothesis Ho.

So we have sufficient evidence at 5% & the popular idea verified.