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College Statistics question - hypothesis testing?
IMMEDIATE BEST ANSWER FOR FIRST CORRECT ANSWER. dont need proof, just answers
GreenBeam Ltd. claims that its compact fluorescent bulbs average no more than 3.54 mg of mercury. A sample of 40 bulbs shows a mean of 3.62 mg of mercury.
1. State the hypotheses for a right-tailed test, using GreenBeams’s claim as the null hypothesis about the mean
2.
Assuming a known standard deviation of 0.17 mg, calculate the z test statistic to test the manufacturer’s claim. (Round your answer to 2 decimal places.)
3. At the 10 percent level of significance (α = 0.1) does the sample exceed the manufacturer’s claim? (Yes / No)
4. find the p value.
THANKS!
ANSWER: Conclusion: H1 is true
Why????
SINGLE SAMPLE TEST, ONE-TAILED, 6 - Step Procedure for t Distributions, "one-tailed test"
Step 1: Determine the hypothesis to be tested.
Lower-Tail
H0: μ ≥ μ0 H1: μ < μ0
or
Upper-Tail
H0: μ ≤ μ0 H1: μ > μ0
hypothesis test (lower or upper) = upper
Step 2: Determine a planning value for α [level of significance] =0.1
Step 3: From the sample data determine x-bar, s and n; then compute Standardized Test Statistic: t = (x-bar - μ0)/(s/SQRT(n))
x-bar: Estimate of the Population Mean (statistical mean of the sample) = 3.62
n: number of individuals in the sample = 40
s: sample standard deviation = 0.17
μ0: Population Mean = 3.54
significant digits =3
Standardized Test Statistic t = ( 3.62 - 3.54 )/( 0.17 / SQRT( 40 )) = 2.976
Step 4: Use Students t distribution, 'lookup' the area to the left of t (if lower-tail test) or to the right of t (if upper-tail test) using Students t distribution Table or Excel TDIST(x, n-1 degrees_freedom, 1 tail) =TDIST( 2.976 , 39 , 1 )
Step 5: Area in Step 4 is equal to P value [based on n -1 = 39 df (degrees of freedom)] = 0.002
Table look-up value shows area under the 39 df curve to the right of t = 2.976 is (approx) probability = 0.002
Step 6: For P ≥ α, fail to reject H0; and for P < α, reject H0 with 90% confidence.
Conclusion: H1 is true
Note: level of significance [α] is the maximum level of risk an experimenter is willing to take in making a "reject H0" or "conclude H1" conclusion (i.e. it is the maximum risk in making a Type I error).
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