Question

You wish to test the following claim (HaHa) at a significance level of α=0.002α=0.002.

      Ho:μ=55.2Ho:μ=55.2
      Ha:μ<55.2Ha:μ<55.2

You believe the population is normally distributed and you know the standard deviation is σ=14.9σ=14.9. You obtain a sample mean of ¯x=47.2x¯=47.2 for a sample of size n=33n=33.

What is the test statistic for this sample?
test statistic = (Report answer accurate to 3 decimal places.)

What is the p-value for this sample?
p-value = Use Technology (Report answer accurate to 4 decimal places.)

The p-value is...

• less than (or equal to) αα
• greater than αα

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 55.2.
• There is not sufficient evidence to warrant rejection of the claim that the population mean is less than 55.2.
• The sample data support the claim that the population mean is less than 55.2.
• There is not sufficient sample evidence to support the claim that the population mean is less than 55.2.

Answer 1

The R-code is

round(pnorm(-3.084),4)