hesis is H : p-0.21 our alternative hypothesis is Hi : p > 0.21 (For this proble
ID: 3340082 • Letter: H
Question
hesis is H : p-0.21 our alternative hypothesis is Hi : p > 0.21 (For this problem, just assume n p (1-p) 10 and n s N/20.) one-tailes (a) State the value of po (b) Should we use a normal distribution jor a t-distribution? (c) Find the critical number(s) (d) What formula should we use for the test statistic? o.21 (e) Use level of significance 0.05. Suppose a sample of 101 individuals yields a sample proportion p = 0.33. First find the value of the test statistic: i. Use the test statistic method to determine whether to reject the null hypothesis i. Use the P-value method to determine whether to reject the null hypothesisExplanation / Answer
4.
a) population proporiton P0 = 0.21
b) Normal continuity condition is satiesfied
so it Normal distribution
c) Critical value: +1.645
d) Test Statistic Z = (p - P0) / sqrt(P0*Q0/n)
e) Test Statistic Z = (0.33 - 0.21) / sqrt(0.21*0.79/101)
= 2.9609
i) Here Z value > Z - critical value, so we reject null hypothesis
ii) P-Value: 0.0019 < alpha 0.05, so we reject null hypothesis
f) Critical z: 2.5758 at alpha = 0.005
i) Here Z value > Z critical value, so we reject null hypothesis
ii) P-Value: 0.0019 < alpha 0.005, so we reject null hypothesis
iii) P-value is easiest method compare to critical value method
5.
a) population proporiton mu0 = 68.68
b) it is used to 't' distribution
c) Critical t: -1.2901 at alpha = 0.1
d) Test Statistic t = (xbar - mu )/ (S/sqrtn))
e) Test Statistic t = (67.43-68.68)/ (3.16/sqrt(101) =-3.9754
i) Here t value < t - critical value, so we reject null hypothesis
ii) P-Value: 0.0001 < alpha 0.1, so we reject null hypothesis
f) Critical t: -2.6259 at alpha =0.005
i) Here t value < t critical value, so we reject null hypothesis
ii) P-Value: 0.0001 < alpha 0.005, so we reject null hypothesis
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