3/28/2016 Chapter 7 Test 7. (a) Write the claim mathematically and identify Ho a
ID: 3150962 • Letter: 3
Question
3/28/2016 Chapter 7 Test 7. (a) Write the claim mathematically and identify Ho and Ha. (b) Find the critical value(s) and identify the rejectiorn region(s). (c) Find the standardized test statistic. (d) Decide whether to reject or fail to reject the null hypothesis An environmental agency recently claimed more than 30% of consumers have stopped buying a certain product because of environmental concerns. In a random sample of 1040 consumers, you find 40% have stopped buying the product. At =0.04, do you have enough evidence to support the claim? (a) Which of the following correctly states Ho and Ha? (0) A. Ho:p 0.30 D. Ho:p= 0.30 B. Ho:p=0.30 Ha: p> 0.30 OE. Ho p2 0.30 Ha p 0.30 Ha ps0.30 OF. Ho pExplanation / Answer
Here we have to test the hypothesis that,
H0 : p <= 0.30 Vs H1 : p > 0.30
where p is population proportion.
Assume alpha = 0.04
Critical value we can find by using EXCEL.
syntax :
=NORMSINV(probability)
where probability = 1 - alpha
Critical value = 1.64
The rejection region is option a).
Because any value greator than 1.64 is rejected.
Therefore option a) is correct.
The test statistic is,
Z = (p^ - p) / sqrt [ (pq) / n ]
p^ = sample proportion = 0.4
p = 0.3
q = 1 - p = 1 - 0.3 = 0.7
n = 1040
Z = (0.4 - 0.3) / sqrt [(0.3*0.7) / 1040 ]
Z = 7.04
Calculated Z > critical value
Reject H0 at 4% level of significance.
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8) Type I error and type II error :
Here we have to test the hypothesis that,
H0 : p < 25% = 0.25 Vs H1 : p >=0.25
We know that,
Type I error = P(Reject H0 / H0 is true)
= P(reject p <=0.25 / p <=0.25)
Reject the claim that p <=0.25 when p is actually less than or equal to 0.25.
A type I error will occur when the actual proportion of new customers who return to buy their next piece of furniture is no more than 0.25 but you reject H0 : p <=0.25.
We know that,
Type II error = P(Accept H0 / H1 is true)
=P( p < 0.25 / p >=0.25 is true)
Accept the claim that p <= 0.25 when p is actually greator than or equal to 0.25.
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Outside : When the standardized test statistic is insode the rejection region, P > alpha.
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