6. Testing Ho : p = 0.75 versus Ha : p > 0.75 when the sample has n = 20, ˆp = 0.50.
(a) Verify that the sample size is large
(b) Find the standard error for ˆp
(c) Find the value of the standardized z-test statistic
a)
here since np=0.75*20 =15 and n(1-p) =20*(1-0.75) =5 ; both are greater than 5; sample size is large
b)
std error se =√(p*(1-p)/n) = sqrt(0.75*0.25/20) = | 0.0968 |
c)
sample proportion p̂ = x/n= | 0.5000 | |
test stat z =(p̂-p)/√(p(1-p)/n)=(0.5-0.75)/0.0968 = | -2.58 |
A hypothesis testing: Ho : p=0.55 HA: p >0.55. We conduct a survey with sample size n =832 and have p =0.75. Find the test statistic z associated with the sample proportion. Note: 1- Only round your final answer to 2 decimal places. Enter your final answer with 2 decimal places.
In a hypothesis testing problem a researcher wants to test the hypothesis Ho 20 versus Ha 20 A sample of size 100 yielded a sample mean x = 19.25 and a sample standard deviation s 2.5. The P-value for the above test is 0013 .5000 0026 0147 0294
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2.11. Suppose that we are testing Ho: μ-μ0 versus H: >o with a sample size of n 15. Calculate bounds on the P-value for the following observed values of the test statistic: (a) to 2.35 (b)o 3.55 (c) 2.00 (d) to 1.55
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