Question

A consulting firm claimed that 65% of all e-commerce shoppers fail in their attempts to purchase merchandise on-line because Web sites are too complex. The claim was tested by taking a random sample of 60 online shoppers and assigning them each a different randomly selected e-commerce Web site to test. 45 reported sufficient frustration with their sites to deter making a purchase. The data was entered into STATISTIX and the following output was generated:
Hypothesis Test - One Proportion

Sample Size 60
Successes 45
Proportion 0.75000

Null Hypothesis: P = 0.65
Alternative Hyp: P > 0.65

Difference 0.10000
Standard Error 0.05590
Z (uncorrected) 1.62 P 0.0522

Method 95% Confidence Interval
Simple Asymptotic (0.64043, 0.85957)

Which of the following statements is correct if we are testing at α = 0.05?

a. There is sufficient evidence to indicate that more than 65% of all e-commerce shoppers fail in their attempts to purchase merchandise on-line because Web sites are too complex.
b. There is sufficient evidence to indicate that exactly 65% of all e-commerce shoppers fail in their attempts to purchase merchandise on-line because Web sites are too complex.
c. There is insufficient evidence to indicate that exactly 65% of all e-commerce shoppers fail in their attempts to purchase merchandise on-line because Web sites are too complex.
d. There is insufficient evidence to indicate that more than 65% of all e-commerce shoppers fail in their attempts to purchase merchandise on-line because Web sites are too complex.

Answer 1

Answer:

b. There is sufficient evidence to indicate that exactly 65% of all e-commerce shoppers fail in their attempts to purchase merchandise on-line because Web sites are too complex.

Step-by-step explanation:

Not significant,accept null hypothesis that population proportion = 0.65

When we accept the null hypothesis that P= 0.65

Then only option b is correct which states that  there is sufficient evidence to support that population proportion is exactly 0.65 .

1) We obtain a P - value of 0.0522 which is greater than 0.5 indicating that the null hypothesis is not rejected.

The rejection region for this right-tailed test is z > 1.64

2) Test Statistics

z= p`-p0/ sqrt(p0(1-p0)/n)

The z-statistic is computed as follows:

z= 0.75-0.65/ √(0.65*0.35)60

z= 1.624

3) Decision about the null hypothesis

Since it is observed that z = 1.624 is less than z ∝=1.64, it is then the null hypothesis is not rejected.