Question

# You wish to test the following claim (HaHa) at a significance level of α=0.002α=0.002.       Ho:μ=68.3Ho:μ=68.3       Ha:μ≠68.3Ha:μ≠68.3...

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

Ho:μ=68.3Ho:μ=68.3
Ha:μ≠68.3Ha:μ≠68.3

You believe the population is normally distributed, but you do not know the standard deviation. You obtain a sample of size n=13n=13 with mean M=73.5M=73.5 and a standard deviation of SD=13.4SD=13.4.

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

The p-value is...

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

This p-value 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 not equal to 68.3.
• There is not sufficient evidence to warrant rejection of the claim that the population mean is not equal to 68.3.
• The sample data support the claim that the population mean is not equal to 68.3.
• There is not sufficient sample evidence to support the claim that the population mean is not equal to 68.3.

solution:

the given information as follows:

sample size = n = 13

sample mean = = 73.5

Sd = S = 13.4

the given null and alternative hypothesis:  significance level = = 0.002

since population standard dviation is not known so we use t-distribution

test statistics: degree of freedom df = n-1 = 13-1 = 12

p value with t = 1.399 and 12df for two taile = 0.1871

p vaue is greater than so, fail reject the null hypothesis

conclusion:

There is not sufficient sample evidence to support the claim that the population mean is not equal to 68.3.

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