Estimation and Hypothesis TestsBased on the instructions now posted in your data set, you will construct a Confidence Interval for one of your quantitative variables and conduct a hypothesis test for the other quantitative variable.For the Confidence Interval:1. Report the interval.2. Interpret the confidence interval in terms of the specific variable.For the Hypothesis Test:1. State the null and alternative hypotheses in the context of the specific variable. 2. Report the t test statistic and its meaning.3. Report the p-value and its meaning.4. Draw your conclusion. Include the comparison of the p-value to the level of significance, whether you reject or fail to reject the null hypothesis, whether the results are statistically significant or not, and your concluding statement in the context of the specific variable. FilterSelectFKFinal Project Part 3Farmland DataAssorted farmland available for purchase from 2013-2018.CI: Construct a 95% confidence interval for theaverage Size of Land available for purchase from2013-2018 in Illinois.Variables:State: U.S. stateTEST: The average Price per Acre of farmland inCalifornia,is $10,000. Do the data indicate that this isdifferent than the Price per Acre in Illinois?Size of Land in Acres: The amount of land availablePrice per Acre in Dollars: The total price of the farmland divided bythe number of acresDate: Month and year that the farmland was available for purchase StateSize of Land in AcresPrice per Acre in Dollars13500DateAugust 2013August 2013Illinois152Illinois33910738Illinois2617600November 2013Illinois33813250December 2013Illinois36210737December 2013Illinois7315000Winter 2014Illinois54212786Winter 2014February 2014February 2014February 2014Illinois592750Illinois143111750Illinois8010750Illinois54212786March 2014Illinois7512100March 2014April 2014May 2014May 2014Illinois7315000Illinois1669009Illinois96014583IllinoisIllinois17613920June 201415535280June 2014July 2014August 2014August 2014Illinois14412900Illinois54013127Illinois8712700Illinois13427086October 2014Illinois1329030October 2014Illinois806400November 2014Illinois7655483December 2014Illinois1168534Winter 2015Illinois29410935February 2015Illinois4026281March 2015Illinois1568250June 2015Illinois819000July 2015Illinois8010400December 2015Illinois33411482Winter 2016Illinois55610775April 2016Illinois15601984June 2016Illinois2179700August 2016September 2016September 2016Illinois15310255Illinois1609000Illinois7510400October 2016Illinois23611100October 2016Illinois4010800November 2016Illinois978750November 2016Illinois2179700December 2016Illinois1609000December 2016February 2017February 2017Illinois86386403Illinois6102925Illinois3077053March 2017Illinois10638982March 2017April 2017April 2017August 2017September 2017Illinois19510097Illinois1618500Illinois11679443Illinois11679426Illinois3208100October 2017Illinois12311745December 2017Illinois15510516February 2018

Name: Estimation and Hypothesis TestsBased on the instructions now posted in
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Description: Estimation and Hypothesis TestsBased on the instructions now posted in your data set, you will construct a Confidence Interval for one of your quantitative variables and conduct a hypothesis test for the other quantitative variable.For the Confidence

Obtain the mean and standard deviation for the size of land in acres for the state Illinois: The data represents the size of land in acres for the state Illinois. Here, EXCEL software is used to calculate the mean and standard deviation for the sample. The step-by-step procedure to obtain mean and standard deviation using EXCEL software is given below: Open an EXCEL file. Enter the data of size of land in column A and name it as Size of land. In the cell B1 enter the formula = AVERAGE (A2-A54) and click on ENTER. In the cell C1 enter the formula =STDEV.S(A2-A54) and click on ENTER. The outputs are shown below: Therefore, the sample mean is x-bar = 549.283. Therefore, the sample standard deviation is s = 1207.1809.Construct a 95% confidence interval for the average size of land available for purchase from 2013-2018 in Illinois: Denote the population mean size of land available for purchase from 2013-2018 in Illinois as µ. Critical value: The level of confidence is 1- α = 0.95. The critical value is obtained as 2.0066 from the calculation given below: The 95% confidence interval for the average size of land available for purchase from 2013-2018 in Illinois is obtained as (216.5505 ≤ µ ≤ 882.0155) from the calculation given below: Thus, the 95% confidence interval for the average size of land available for purchase from 2013-2018 in Illinois is (216.5505 ≤ µ ≤ 882.0155). Interpretation: One can be 95% confident that the average size of land available for purchase in Illinois from 2013-2018 lies between 216.5505 acres and 882.0155 acres.Obtain the mean and standard deviation for the price per acre in dollars for the state Illinois: The data represents the price per acre in dollars for the state Illinois. Here, EXCEL software is used to calculate the mean and standard deviation for the sample. The step-by-step procedure to obtain mean and standard deviation using EXCEL software is given below: Open an EXCEL file. Enter the data of price per acre in column A and name it as Price per acre. In the cell B1 enter the formula = AVERAGE (A2-A54) and click on ENTER. In the cell C1 enter the formula =STDEV.S(A2-A54) and click on ENTER. The outputs are shown below: Therefore, the sample mean is x-bar = 9769.8302. Therefore, the sample standard deviation is s = 2965.7053.Null and alternate hypotheses: The investigator is interested to test whether the population mean price per acre of farmland in Illinois is different from the average price per acre of farmland in California. Denote the population mean price per acre of farmland in Illinois as μ. Given that the average price per acre of farmland in California is $10,000. The hypotheses are given below: Null hypothesis: H0 : μ = 10,000 That is, the population mean price per acre of farmland in Illinois is equal to $10,000. Alternative hypothesis: Ha : μ ≠ 10,000 (Two tail test). That is, the population mean price per acre of farmland in Illinois is significantly different from $10,000.Type of test statistic: The objective is to test for the significance of population mean. Here, the population standard deviation is unknown and the population from which the sample is drawn follows approximately normal distribution. Thus, a single sample t test is appropriate for the given situation. Test statistic: The sample size is n = 54. The sample mean is x-bar = 9769.8302. The sample standard deviation of difference is s = 2965.7053. The test statistic value is obtained as -0.565 from the calculations given below: Thus, the value of test statistic is t = -0.565. Interpretation: The measure of degree of agreement between a sample of data and the null hypothesis is t = -0.565.P-value: The critical value is obtained as 0.5745 from the calculation given below: Thus, the P-value is 0.5745. Interpretation of P-value: The p-value is the probability of obtaining a value (statistic) of the test result as extreme as, or more extreme than, the value that has been obtained, assuming H0 to be true. So, the p-value is not the probability of making a mistake. It is just a probability of getting a certain result when H0 is true. Thus, there is 0.5745 probability of obtaining a test statistic -0.565 of the test result as extreme as, or more extreme than, the value that has been obtained, assuming H0 to be true.Decision rule: Since, the level of significance is not specified, the prior level of significance α = 0.05 can be used. Decision rule based on P-value approach: If P-value ≤ α, then reject the null hypothesis H0. If P-value > α, then fail to reject the null hypothesis H0. Conclusion: Conclusion based on P-value approach: The P-value is 0.5745 and α value is 0.05. Here, P-value is greater than the α value. That is, 0.5745 (=P-value) > 0.05 (=α). By the rejection rule, fail to reject the null hypothesis. Thus, the population mean price per acre of farmland in Illinois is equal to $10,000. Hence, there is not enough evidence to conclude that the average price per acre farmland in Illinois is different from the average price per acre of farmland in California.