For the loan amounts, what is the sample mean, the sample standard deviation, and the sample size? Can you assume normality to use the normal distribution? Explain why?. Calculate a $95\%$ confidence interval estimate of the population mean from this sample. HINT: Use the Excel Calculator for Population Mean Interval Estimation Calculator $-$ Sigma unknown Interpret your interval estimate using proper terminology. You can refer to your My Lab work for help. A Banking Industry report came out saying most banks averaged less than $$55,000$ in their loans made last year. Use your confidence interval to decide whether Society Bank is $$most banks?$$ Explain your rationale. Use the reported average loan amount of $$55,000$ by the banking industry to test to see if Society Bank loans are higher on average than the industry as a whole. Use $\backslash$alpha $=0\mathrm{.}05$ State the hypotheses. You need null and alternative hypotheses. Use the Excel Calculator for hypothesis testing a population mean. Save your file and upload it with your report. write your conclusions including your p$-$value, test statistic, and level of significance. How many loans are real estate loans, and what is the sample proportion of real estate loans? Calculate a $95\%$ confidence interval for the proportion of loans which are real estate loans. Show your work. HINT: Use the Excel Population Proportion Interval Estimation Calculator. Interpret your interval estimate using proper terminology. A Banking Industry report claimed at least $50\%$ of loans are commercial loans. Test this claim with $\backslash$alpha $=0\mathrm{.}05$ to answer the question: Are commercial loans less than half of all loans? State the hypotheses. You need null and alternative hypotheses. Use the Excel Calculator for hypothesis testing a population proportion. Save your file and upload it with your report. Write your conclusions including your p$-$value, test statistic, and level of signLoan.

Loan Amount Type Region Follow Box $2$ follow box $3$

$$33,000\mathrm{.}00$ Consumer $1$ $$125,000\mathrm{.}00$ Real Estate $3$ $$72,000\mathrm{.}00$ Consumer $3$

$$30,500\mathrm{.}00$ Commercial $1$ $$74,000\mathrm{.}00$ Real Estate $2$ $$92,500\mathrm{.}00$ Commercial $3$

$$84,500\mathrm{.}00$ Commercial $2$ $$59,000\mathrm{.}00$ Commercial $3$ $$56,500\mathrm{.}00$ Consumer $3$

$$110,500\mathrm{.}00$ Commercial $3$ $$31,500\mathrm{.}00$ Commercial $3$ $$83,500\mathrm{.}00$ Consumer $1$

$$21,500\mathrm{.}00$ Commercial $3$ $$82,500\mathrm{.}00$ Commercial $2$ $$91,000\mathrm{.}00$ Commercial $1$

$$59,500\mathrm{.}00$ Commercial $4$ $$86,500\mathrm{.}00$ Commercial $2$ $$122,000\mathrm{.}00$ Commercial $2$

$$48,500\mathrm{.}00$ Real Estate $1$ $$10,000\mathrm{.}00$ Commercial $2$ $$23,000\mathrm{.}00$ Commercial $1$

$$57,000\mathrm{.}00$ Commercial $2$ $$52,500\mathrm{.}00$ Consumer $2$ $$38,500\mathrm{.}00$ Commercial $1$

$$116,000\mathrm{.}00$ Commercial $3$ $$73,000\mathrm{.}00$ Commercial $1$ $$45,500\mathrm{.}00$ Consumer $3$

$$89,500\mathrm{.}00$ Consumer $1$ $$58,500\mathrm{.}00$ Consumer $2$ $$101,000\mathrm{.}00$ Consumer $1$

$$40,000\mathrm{.}00$ Consumer $1$ $$31,500\mathrm{.}00$ Commercial $2$ $$44,000\mathrm{.}00$ Commercial $2$

$$117,500\mathrm{.}00$ Real Estate $1$ $$41,000\mathrm{.}00$ Consumer $3$ $$76,500\mathrm{.}00$ Consumer $2$

$$78,500\mathrm{.}00$ Commercial $1$ $$15,500\mathrm{.}00$ Consumer $1$ $$95,000\mathrm{.}00$ Commercial $4$

$$76,000\mathrm{.}00$ Consumer $1$ $$7,000\mathrm{.}00$ Consumer $3$ $$62,000\mathrm{.}00$ Consumer $1$

$$90,000\mathrm{.}00$ Commercial $1$ $$41,500\mathrm{.}00$ Commercial $2$ $$96,000\mathrm{.}00$ Commercial $1$

$$19,000\mathrm{.}00$ Commercial $1$ $$39,000\mathrm{.}00$ Commercial $2$ $$33,000\mathrm{.}00$ Commercial $2$

$$72,500\mathrm{.}00$ Consumer $1$ $$35,000\mathrm{.}00$ Consumer $3$ $$75,500\mathrm{.}00$ Consumer $1$

$$57,000\mathrm{.}00$ Real Estate $1$ $$86,000\mathrm{.}00$ Commercial $4$ $$18,500\mathrm{.}00$ Consumer $1$

$$102,500\mathrm{.}00$ Real Estate $2$ $$94,500\mathrm{.}00$ Consumer $1$ $$56,000\mathrm{.}00$ Consumer $1$

$$36,000\mathrm{.}00$ Commercial $1$ $$119,000\mathrm{.}00$ Real Estate $1$ $$81,500\mathrm{.}00$ Real Estate $3$

$$123,500\mathrm{.}00$ Consumer $1$ $$63,500\mathrm{.}00$ Real Estate $3$ $$120,500\mathrm{.}00$ Real Estate $1$

$$9,000\mathrm{.}00$ Consumer $1$ $$40,500\mathrm{.}00$ Commercial $3$ $$65,000\mathrm{.}00$ Commercial $3$

$$31,000\mathrm{.}00$ Commercial $4$ $$17,500\mathrm{.}00$ Commercial $1$ $$66,500\mathrm{.}00$ Consumer $1$

$$5,500\mathrm{.}00$ Consumer $2$ $$91,000\mathrm{.}00$ Commercial $1$ $$7,500\mathrm{.}00$ Commercial $3$

$$29,000\mathrm{.}00$ Commercial $2$ $$23,500\mathrm{.}00$ Commercial $1$ $$42,500\mathrm{.}00$ Consumer $1$

$$82,000\mathrm{.}00$ Real Estate $1$ $$102,500\mathrm{.}00$ Real Estate $2$ $$91,000\mathrm{.}00$ Commercial $1$

$$10,500\mathrm{.}00$ Consumer $4$ $$73,500\mathrm{.}00$ Commercial $3$ $$16,500\mathrm{.}00$ Commercial $1$

$$72,000\mathrm{.}00$ Commercial $3$ $$111,000\mathrm{.}00$ Commercial $1$ $$97,000\mathrm{.}00$ Commercial $2$

$$67,000\mathrm{.}00$ Commercial $4$ $$20,000\mathrm{.}00$ Consumer $1$ $$103,000\mathrm{.}00$ Commercial $2$

$$6,500\mathrm{.}00$ Consumer $1$ $$21,500\mathrm{.}00$ Commercial $3$ $$76,500\mathrm{.}00$ Consumer $4$

$$28,500\mathrm{.}00$ Commercial $4$ $$29,000\mathrm{.}00$ Real Estate $2$ $$44,500\mathrm{.}00$ Consumer $1$

$$113,500\mathrm{.}00$ Consumer $1$ $$93,000\mathrm{.}00$ Real Estate $1$ $$72,500\mathrm{.}00$ Consumer $1$

$$99,000\mathrm{.}00$ Real Estate $3$ $$40,500\mathrm{.}00$ Commercial $2$ $$20,000\mathrm{.}00$ Consumer $1$

$$93,500\mathrm{.}00$ Real Estate $3$ $$66,500\mathrm{.}00$ Commercial $1$ $$6,000\mathrm{.}00$ Commercial $3$

$$102,000\mathrm{.}00$ Consumer $4$ $$11,000\mathrm{.}00$ Real Estate $1$ $$17,000\mathrm{.}00$ Real Estate $4$

$$94,000\mathrm{.}00$ Consumer $2$ $$90,000\mathrm{.}00$ Consumer $3$ $$36,000\mathrm{.}00$ Commercial $1$

$$89,500\mathrm{.}00$ Commercial $1$ $$76,000\mathrm{.}00$ Consumer $4$ $$49,000\mathrm{.}00$ Consumer $3$

$$66,500\mathrm{.}00$ Commercial $3$ $$21,000\mathrm{.}00$ Commercial $1$ $$70,500\mathrm{.}00$ Commercial $4$

$$22,000\mathrm{.}00$ Commercial $1$ $$69,000\mathrm{.}00$ Commercial $2$ $$96,000\mathrm{.}00$ Commercial $1$

$$107,000\mathrm{.}00$ Consumer $3$ $$81,500\mathrm{.}00$