Explain step by step how to solve problem 114÷6114÷6
2 answers:
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Answer:
The test statistic t = 1.219 < 2.262 at 5% level of significance
we accept significance of level that the population mean is less than 20.
Step-by-step explanation:
Given ages are 22, 17, 27, 20, 23, 19, 24, 18, 19, and 24
The random sample (n) = 10
Null hypothesis (H0): μ = 20
Alternative hypothesis(H1) : μ < 20 (left tailed test)
we will use statistic 't' distribution with small sample 10 < 30
mean (χ) = sum of observations divided by no of observations
mean(x) = ∑x / n =
x x - mean (x-mean)^2
22 22-21.3 = 0.7 0.49
17 17-21.3 = -4.3 18.49
27 27-21.3 = 5.7 32.49
20 20-21.3 =-1.3 1.69
23 23-21.3 = 1.7 2.89
19 19-21.3 = -2.3 5.29
24 24-21.3 = 2.7 7.29
18 18-21.3 = -3.3 10.89
19 19-21.3 = -2.3 5.29
24 24-21.3 = -=2.7 7.29
S = 3.198
The test statistic (t) =
t = 1.219
The degrees of freedom = n-1 = 10-1 =9
Tabulated value of t for 9 degrees of freedom at 5% level of significance
= 2.262
since calculated t < tabulated t we accept the null hypothesis
we accept significance of level that the population mean is less than 20.