Answer to Question #295513 in Statistics and Probability for Ace

Question #295513

. The average family size in the Philippines was reported as 4.25. A random of families in a particular street resulted in the following family sizes: 5, 6, 7, 4, 3, 2, and 9. At 𝛼=0.10, does the average family size more than the national average?


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Expert's answer
2022-02-10T03:40:53-0500

n=7xΛ‰=βˆ‘xn=367=5.14285714s2=βˆ‘x2βˆ’(βˆ‘(x))2nnβˆ’1=220βˆ’185.1428576=5.8095s=s2=5.8095=2.4103n=7\\\bar x={\sum x\over n}={36\over7}=5.14285714\\ s^2={\sum x^2-{(\sum(x))^2\over n}\over n-1}={220-185.142857\over6}=5.8095\\s=\sqrt{s^2}=\sqrt{5.8095}=2.4103

The hypotheses are,

H0:ΞΌ=4.25vsH1:ΞΌ>4.25H_0:\mu=4.25\\vs\\H_1:\mu\gt4.25

The test statistic is,

t=xΛ‰βˆ’ΞΌsn=5.14βˆ’4.252.41037=0.89290.911=0.98t={\bar x-\mu\over {s\over\sqrt{n}}}={5.14-4.25\over{2.4103\over\sqrt{7}}}={0.8929\over0.911}=0.98

The critical value is,

tΞ±,nβˆ’1=t0.1,6=1.439756t_{\alpha,n-1}=t_{0.1,6}=1.439756

The null hypothesis is rejected if, t>t0.1,6t\gt t_{0.1,6}

Since t=0.98<t0.1,6=1.439756t=0.98\lt t_{0.1,6}=1.439756, the null hypothesis is not rejected. Therefore, we can conclude that there is no sufficient evidence to show that the average family size is more than the national average at 1% level of significance.


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