Question

2 of 2 (2 complete HW Score: 50%, 1 Score: 0 of 1 pt Ostion Hel X 8.4.46-T A bank report looks at what wrategies and measures ancial institutions are pursuing to provide mobile financial services to their customers in a response to a survey question about bams hindering greater consumerado mobile banking in a survey of 123 fancial institutions, 83 said security concerns are a barrier 74 said lack of trust in the technology is a barrier and 23 saddloutyou w a barrier Complete parts og below Construct a confidence intervalimate of the population proportion of financial institutions who said that security concerns are a barrier hindering greater consume adoption of mobile banking 0606 SES 0744 Round to three decimal places needed) b. Constructa 90% confidence intervalestimate of the population proportion of facilities who said that lack of trust is a barrier hindering or consumer adaption of mobile banking S o und to the decimal places as needed

Answer 1

Sample size, n = 123

Number of customer saying lack of trust is a barrier = 74

We need to construct the 90% confidence interval for the population proportion. We have been provided with the following information about the number of favorable cases:

Favorable Cases X	74
Sample Size N	123

The sample proportion is computed as follows, based on the sample size N = 123 and the number of favorable cases X = 74:

P = N

74 p = 123

p0.602

The critical value for $\alpha = 0.1$ is . The corresponding confidence interval is computed as shown below:

21-a/2 1.645

p(1 — Р) Р(1 - р) CI (Proportion

0.6021 0.602) 0.602(1 0.602) CI (Proportion) , 0.602 1.645 x 0.602 1.645 x 123 123

CI(Proportion) = (0.529,0.674

Therefore, based on the data provided, the 90% confidence interval for the population proportion is 0.529 < p < 0.674, which indicates that we are 90% confident that the true population proportion pp is contained by the interval (0.529, 0.674).