It has been hypothesized that houses with fireplaces are larger than houses without fireplaces. 1. [25 points, 12.5 per bound] Create a 95% confidence interval for living area (sq. ft.) of houses with fireplaces: Lower Bound: 1946. 043 Upper Bound: 2023. 603 2. [10 points] What does this 95% confidence interval tell you about the living area of houses with fireplaces ? I am 95% confident that the menliving area her homes wihreplaces for this speatie sale is between 1946.0413 SEPE and 2023.603sq et : 3. [25 points, 12.5 per bound] Create a 95% confidence interval for living area (sq. ft.) of houses without fireplaces: Lower Bound: 1414.349 Upper Bound: 1481 - 847 4. [10 points] What does this 95% confidence interval tell you about the living area of houses without fireplaces ? I am 9590 confident that me mean are in sack of living space for haves what freplaces is between 1414. 34x 9 sell and 1481-847SERE. 5. [10 points, 5 for reasoning] Do you believe that houses with fireplaces are larger than houses without fireplaces based on these confidence intervals? Explain your reasoning. Based on my facts collected above through the we of confidence levels I can see that yes, haves with Rreplaces are larger than houses willart fireplaces. I am able to confirm this by comparing the figures gathered Per harees what Areplaces and moreliving space which care me a range of confidence from 1414. 349 to $8 1481-847 which dearly is love than the rage of living space gathered for haves wifreplaces which gave me condodance at 1946. 0413 s s to 2023.603. When we audley look at the figures andCompare it is door that haves w hreplaces have a hugher range in confidence levels compared to haves withat fireplaces and Morehere we can Continue based on 95%% confidence that Games wihreplace do in Pack have a larger living area based on this saple and question.Perform a hypothesis test at the a = .05 significance level to test the claim that houses with fireplaces have more living area (in square footage) than houses without fireplaces. a. [20 points, 10 each] Write the hypotheses: Ho: Nullhypothesis Hi: Alternative luporhesus ; we the researcher are looking totest Medain Ther haves wihreplaces have more living space area (insEff ) Muonhouses war Rreplaces . b. [10 points] What is the value of your test statistic? The value of air test statishe is 20- 528. This means or sayde mean is nerdy 20.528 st.deviation more then what we would expect if all living area in salt exceeded the sale mean of 1985 555 salt. c. [10 points] What is your P-value? My Pradue is the probability of doserving saple mean as unlikely or me unlikely than there we computed from the sample collected assuming null is true. we get this value by using excel to this formula - T.dist ( absvalue, desnees of feeder, number of tails ) = 1.9 96-74 d. [10 points] Do you reject the null hypothesis or fail to reject the null hypothesis at the a = .05 significance level? The rest is at a 0.05 signingance level. The pralue is ,-qaEfl which is more Then 0.05 signingonce level and so we can Mireferce accept the null hypothesis as mere is enough auguricontendence to support, the daim more haves wl fireplaces have a large living space e. [20 points] Do you believe that houses with fireplaces are larger than houses without fireplaces based on the outcome of this hypothesis test? Explain your reasoning. Thetest In regards to the suchen there is significant enderce to support not the homes wl freplaces have a longer living area ( so RX ) then haves wlair fireplaces, we can determine this because of our t-test on the given dara / info and by testing the alternative hypothesis which we know was the mean sE Profliving area greater men 1985.55, This test allowed us to see that ara 0.05 signincance level and a pvalue of 1. 99098 5-74 was higher than the significance and because of this we except the null to confirm there is not enough evidence to support the daimPOPULATION VS. SAMPLE opulation All home in Saratoga County NY Sample All homes in Saratoga County NY that have homes with fireplaces ARIABLE ariable arameter tatistic x-bar AMPLE DATA ample Mean x-bar 1984.822874 ample St Dev S 620.8461608 ample Size 987 ONDITIONS Random or representative sample Satisfied as the Information states a random sample is taken Sample size n is at least 30 OR the population is approximately normal Satisfied as the sample size is over 30, It Is 987 Sample size n is less than 10% of the population Satisfied as the sample size is less than the population, It Is 9870 9870 If population size exceeds this number, then Condition 3 is satisfied ONFIDENCE INTERVAL onfidence Level 95% all Area 0.05 egrees of Freedom df 986 Critical Value 1.962 OWER BOUND 1946.043 PPER BOUND 2023.603 ITERPRETATION We are 95% confident that the mean sq it of living space for homes with fireplaces is between [lower bound] 1946.043 and [upper bound] 2023.603. alactions for haves wihreplacesPOPULATION VS. SAMPLE Population All home in Saratoga County NY Sample All homes in Saratoga County NY that have homes without fireplaces VARIABLE Variable Parameter Statistic x-bar SAMPLE DATA Sample Mean x-bar 1448.098649 Sample St Dev S 467.332733 Sample Size n 739 CONDITIONS Random or representative sample Satisfied, this is a random sample as stated in the text Sample size n is at least 30 OR the population is approximately normal Satisfied, the sample size is more than 30 as it is 739 Sample size n is less than 10% of the population Satisfied as the sample size is less than 10% of the population it is 7390 7390 If population size exceeds this number, then Condition 3 is satisfied CONFIDENCE INTERVAL Confidence Level 0.95 Tail Area 0.05 Degrees of Freedom df 738 t Critical Value 1.96318363 LOWER BOUND 1414.34934 UPPER BOUND 1481.84796 INTERPRETATION We are 95% confident that the mean sq ft of living area for homes without fireplaces is between [lower bound]1414.349 and [upper bound]1481.847. Calculates for haves what hreplaces in SaratogaPOPULATION VS. SAMPLE Population 1 Homes in Saratoga with and without fireplaces Sample 1 Homes in Saratoga with fireplaces Population 2 Homes in Saratoga with and without fireplaces Sample 2 Homes in Saratoga without fireplaces VARIABLE Variable sq ft (living space) Parameter 1 H1 Mean sq ft of living space for all homes in Saratoga with and without fireplaces Mean [variable] for [population 1] Statistic 1 x-bar1 Mean sq ft of living space for all homes in Saratoga with fireplaces Mean [variable] for [sample 1] Parameter 2 H2 Mean sq ft of living space for all homes in Saratoga with and without fireplaces Mean [variable] for [population 2] Statistic 2 x-bar2 Mean sq ft of living space for all homes in Saratoga without fireplaces Mean [variable] for [sample 2] SAMPLE DATA Sample Mean 1 x-bar] 1985.555 Sample St Dev 1 $1 20.397 Sample Size 1 987 Sample Mean 2 x-bar2 1448.099 Sample St Dev 2 $2 67.333 Sample Size 2 n2 739 HYPOTHESES Null Hypothesis HO H2 Initially assumed to be true Alternative Hypothesis H1 H1 " =/=" H2 Tails CONDITIONS Representative Both samples are random or representative Satisfied as both samples are random, it is stated in the text Yes Samples are independent Satisfied, as samples are independent 201>30, 153>30 Both sample sizes are at least 30 OR the populations are approximately normal Satisfied as both samples are over 30 Absolutely Each sample size is less than 10% of the population Satisfied as both samples sizes are less than 10% of the population 9870 If population 1 size exceeds this number and population 2 exceeds the number below, then Condition 4 is satisfied 7390 TEST STATISTIC & P-VALUE Test statistic 20.528 Absolute value It| 20.528 Degrees of freedom df 738 Number of tails P-value 0.00000000 1.99098E-74 Significance level 0.05000000 DECISION P-val