You wish to test the following claim (HaHa) at a significance level of =0.002=0.
ID: 3269493 • Letter: Y
Question
You wish to test the following claim (HaHa) at a significance level of =0.002=0.002.
Ho:1=2Ho:1=2
Ha:12Ha:12
You believe both populations are normally distributed, but you do not know the standard deviations for either. And you have no reason to believe the variances of the two populations are equal You obtain a sample of size n1=24n1=24 with a mean of ¯x1=61.6x¯1=61.6 and a standard deviation of s1=10.1s1=10.1 from the first population. You obtain a sample of size n2=28n2=28 with a mean of ¯x2=64x¯2=64 and a standard deviation of s2=18.4s2=18.4 from the second population.
What is the test statistic for this sample?
test statistic = Round to 4 decimal places.
What is the p-value for this sample?
p-value = 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 first population mean is not equal to the second population mean.
There is not sufficient evidence to warrant rejection of the claim that the first population mean is not equal to the second population mean.
The sample data support the claim that the first population mean is not equal to the second population mean.
There is not sufficient sample evidence to support the claim that the first population mean is not equal to the second population mean
Explanation / Answer
From information given, samples are independent, and both populations are normally distributed, assume unequal variance. Thus, the non-pooled t test statistic is as follows:
t=(x1bar-x2bar)/sqrt[s1^2/n1+s2^2/n2], where, xbar is sample mean, s is sample standard deviation, n is sample size and 1, 2 denote sample 1 and 2 respectively.
=(61.6-64)/sqrt[10.1^2/24+18.4^2/28]
=-0.5900
p value at 43 degrees of freedom is 0.5560.
[df=(s1^2/n1+s2^2/n2)^2/{1/n1-1(s1^2/n1)^2+1/n2-1(s2^2/n2)^2}]
The p value is greater than alpha=0.002.
Per rejection rule based on p value, reject null hypothesis if p value is less than alpha. Here, p value is not less than alpha=0.002. Therefore, fail to reject null hypothesis.
Since, one fail to reject null hypothesis, there is insufficient evidence to warrant the rejection of null hypothesis. Thus, option 1 and 3 are discarded. Option 2 wrongly supports alternative hypothesis. Option 4 is therefore, correct.
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