Jon wants to know if people who live alone have more pets than people who live w
ID: 3225726 • Letter: J
Question
Jon wants to know if people who live alone have more pets than people who live with others. To test this hypothesis, Jon collects data from a random sample of n = 122 Americans. He finds that 61 people in his sample live alone and have a mean number of pets of M = 1.5 with a standard deviation of s = 0.5. He finds that n = 61 people in his sample live with others and have a mean number of pets of M = 1 with a standard deviation of s = 1. Jon wants to conduct an independent samples t-test to see if results suggest that people who live alone have significantly (a = .01) more pets than people who live with others. Jon computes a t-observed (Step 3) for his sample of 2.890. What is the effect size (r^2) for this t-test? Explain what it tells you about the differences/variance in number of pets.Explanation / Answer
Solution:-
State the hypotheses. The first step is to state the null hypothesis and an alternative hypothesis.
Null hypothesis: Alone< Other
Alternative hypothesis: Alone > Other
Note that these hypotheses constitute a one-tailed test.
Formulate an analysis plan. For this analysis, the significance level is 0.01. Using sample data, we will conduct a two-sample t-test of the null hypothesis.
Analyze sample data. Using sample data, we compute the standard error (SE), degrees of freedom (DF), and the t statistic test statistic (t).
SE = sqrt[(s12/n1) + (s22/n2)]
SE = 0.14315
DF = 120
t = [ (x1 - x2) - d ] / SE
t = 3.49
where s1 is the standard deviation of sample 1, s2 is the standard deviation of sample 2, n1 is the size of sample 1, n2 is the size of sample 2, x1 is the mean of sample 1, x2 is the mean of sample 2, d is the hypothesized difference between population means, and SE is the standard error.
The observed difference in sample means produced a t statistic of 3.49. We use the t Distribution Calculator to find P(t > 3.49) = 0.000338
Interpret results. Since the P-value (0.00034) is less than the significance level (0.01), we have to reject the null hypothesis.
From the above test we have sufficient evidence in the favor of the claim that mean number of pets for people living alone is mor ethan the people living with others.
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