Question

8. You wish to test the following claim (HaHa) at a significance level of ?=0.005?=0.005.      

Ho:?=84.5Ho:?=84.5

Ha:?<84.5Ha:?<84.5

You believe the population is normally distributed, but you do not know the standard deviation. You obtain a sample of size n=6n=6 with mean ¯x=60x¯=60 and a standard deviation of s=18.2s=18.2.

What is the test statistic for this sample?

test statistic =_____ Round to 3 decimal places

What is the p-value for this sample?

p-value = _____ Use Technology Round to 4 decimal places.

The p-value is...

less than (or equal to) ??

greater than ?

This test statistic leads to a decision to...

reject the null

accept the null

fail to reject the null

As such, the final conclusion is that...

There is sufficient evidence to warrant rejection of the claim that the population mean is less than 84.5.

There is not sufficient evidence to warrant rejection of the claim that the population mean is less than 84.5.

The sample data support the claim that the population mean is less than 84.5.

There is not sufficient sample evidence to support the claim that the population mean is less than 84.5.

Answer 1

• Since the population is normally distributed and standard deviation was unknown.
• The normality of the population is an important assumption for the validity of the “t test” especially when the sample size is very small, for example, in single figures
• However the “t test” is quite robust against departures from normality especially as the sample size increases
• H0: vs H1 :
• The test statistics is given by
• 
• now substituting the values test statistics obtained is given by
• 
• To calculate the p value we will use numerical method
• from the t distribution table at 5 degrees of freedom and lower 1% the z value is -3.365
• and at lower 2.5% level the z value is -2.571
• therefore to calculate the p value
• 
• =0.02295
• The p value obatined is greater than 0.5% ignificant level
• Therefore we do not have enough evidence to reject null hypothesis.
• Therefore we conclude population mean is equal to 84.5