Question

Research shows that many banks are unwittingly training their online customers to take risks with their passwords and other sensitive account information, leaving them more vulnerable to fraud (Yahoo.com, July 23, 2008). Even web-savvy surfers could find themselves the victims of identity theft because they have been conditioned to ignore potential signs about whether the banking site they are visiting is real or a bogus site served up by hackers. Researchers at the University of Michigan found design flaws in 78% of the 214 U.S. financial institution websites they studied. Is the sample evidence sufficient to conclude that more than three out of four financial institutions that offer online banking facilities are prone to fraud? Use a 5% significance level for the test. (You may find it useful to reference the appropriate table: z table or t table)

a. Select the null and the alternative hypotheses. H0: p = 0.75; HA: p ≠ 0.75 H0: p ≤ 0.75; HA: p > 0.75 H0: p ≥ 0.75; HA: p < 0.75

b. Calculate the sample proportion. (Round your answer to 2 decimal places.)

c. Calculate the value of test statistic. (Round intermediate calculations to at least 4 decimal places and final answer to 2 decimal places.)

d. Find the p-value. p-value < 0.01 0.01 ≤ p-value < 0.025 0.025 ≤ p-value < 0.05 0.05 ≤ p-value < 0.10 p-value ≥ 0.10

e. At the 5% level of significance, what is the conclusion? Reject H0; the claim is supported by the data. Reject H0; the claim is not supported by the data. Do not reject H0; the claim is supported by the data. Do not reject H0; the claim is not supported by the data.

Answer 1

Since sample size is large we use central limit theorem. Hence here we use z test to test the hypothesis. Give thumb up. Thank you