The following information is given 005 The test statistic h

The following information is given:

= 0.05

The test statistic has a standard normal distribution (if H₀ is true).

The sample consists of 232 people who attended one of Taylor Swift’s concerts at MetLife Stadium last July. Their mean age is 19.4 years.

If it is possible to determine the critical value(s) based on this information, determine it/them. If it is not possible, explain why it is not possible.

Solution

Yes we can find critical value by using this information.

We have given that,

= 0.05

The test statistic has a standard normal distribution (if H0 is true).

sample size = 232

mean age = 19.4 years

For finding critical value we need only .

We can find critical value by using EXCEL.

There are three cases for finding critical value :

i) If alternative hypothesis is left tailed then,

EXCEL syntax is,

NORMSINV(probability)

where, probability = 0.05

So, for left tailed test critical value is -1.645.

ii) If alternative hypothesis is right tailed then,

EXCEL syntax is,

NORMSINV(probability)

where, probability = 1 - = 1 - 0.05 = 0.95

So, for right tailed test critical value is 1.645.

iii) If alternative hypothesis is two tailed then,

EXCEL syntax is,

NORMSINV(probability)

where, probability = 1 - /2 = 1 - (0.05/2) = 0.975

So, for two tailed test critical value is 1.96