It has been estimated that about half of prospective on-line customers select it
ID: 3154586 • Letter: I
Question
It has been estimated that about half of prospective on-line customers select items and then cancel their transactions. Suppose that a company changed its Web site so that customers could use a single-page checkout process rather than multiple pages. A sample of 1600 customers who had selected their products were provided with the new checkout system. Of these 1600 customers, 752 cancelled their transactions after they had selected their products. Complete parts (a) through (c) below. a. At the 0.05 level of significance, is there evidence that the population proportion of customers who select products and then cancel their transaction is less than 0.50 with the new system? What are the correct hypotheses to test to determine if the proportion is less? Calculate the test statistic. Z_STAT= What is the p-value? p-value = State the conclusion of the test. the null hypothesis that the proportions are equal. There is evidence to conclude that the population proportion of customers who select products and then cancel their transaction is less than 0.50 with the new system. b. Suppose that a sample of n = 200 customers (instead of n= 1600 customers) were provided with the new checkout system and that 94 of those customers cancelled their transactions after they had selected their products. At the 0.05 level of significance, is there evidence that the population proportion of customers who select products and then cancel their transaction is less than 0.50 with the new system? Calculate the test statistic for the smaller sample. Z_STAT = What is the p-value for the smaller sample? p-value = State the conclusion of the test using this smaller sample at the 0.05 level of significance. the null hypothesis that the proportions are equal. There is evidence to conclude that the population proportion of customers who select products and then cancel their transaction is less than 0.50 with the new system. c. Compare the results of (a) and (b) and discuss the effect that sample size has on the outcome, and, in general, in hypothesis testing. A. The sample proportion is somewhat more probable with the smaller sample size in (b), but this is not enough of an effect to make the conclusions differ. B. Although the sample proportions are the same in both parts, the sample proportion is less probable with the smaller sample size in (b) and so the conclusions differ. C. Since the sample proportions are different, the conclusions are different. This illulstrates the fact that sample sizes are generally irrelevant when n greaterthanorequalto 30. D. Since the sample proportions are the same, the conclusions are the same. This illulstrates the fact that sample sizes are generally irrelevant when n greaterthanorequalto 30. E. Although the sample proportions are the same in both parts, the sample proportion is more probable with the smaller sample size in (b) and so the conclusions differ.Explanation / Answer
Set Up Hypothesis
Null, H0:P=0.5
Alternate, cancelled transaction is less than 0.50 H1: P<0.5
Test Statistic
No. Of Success chances Observed (x)=752
Number of objects in a sample provided(n)=1600
No. Of Success Rate ( P )= x/n = 0.47
Success Probability ( Po )=0.5
Failure Probability ( Qo) = 0.5
we use Test Statistic (Z) for Single Proportion = P-Po/Sqrt(PoQo/n)
Zo=0.47-0.5/(Sqrt(0.25)/1600)
Zo =-2.4
| Zo | =2.4
Critical Value
The Value of |Z | at LOS 0.05% is 1.64
We got |Zo| =2.4 & | Z | =1.64
Make Decision
Hence Value of | Zo | > | Z | and Here we Reject Ho
P-Value: Left Tail -Ha : ( P < -2.4 ) = 0.0082
Hence Value of P0.05 > 0.0082,Here we Reject Ho
[ANSWERS]
a. H0:P=0.5, H1: P<0.5
b. Zo =-2.4
c. ( P < -2.4 ) = 0.0082
d. Reject, there is evidence
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