Americans spend nearly $7 billion on Halloween costumes and decorations. Sample data showing the amount, in dollars, 16 adultsspent on a Halloween costume are as follows.主ili21311530534771331533624696271166a. What is the estimate of the population mean amount adults spend on a Halloween costume (to 2 decimals)?b. What is the sample standard deviation (to 2 decimals)?c. Provide a 95% confidence interval estimate of the population standard deviation for the amount adults spend on a Halloweencostume (to 2 decimals).<σ<

The data shows the amount in dollars of 16 adults spent on a Halloween costume.a. The estimate of the population mean amount adults spend on a Halloween costume is, x¯=∑xn=15+71+21+62+30+33+31+46+53+15+11+96+47+33+66+2716=65716=41.0625≈41.06 Thus, the estimate of the population mean amount adults spend on a Halloween costume is $41.06.b. The sample standard deviation is, s=∑x-x¯2n-1=15-41.06252+71-41.06252+21-41.06252+62-41.06252+30-41.06252+33-41.06252+31-41.06252+46-41.06252+53-41.06252+15-41.06252+11-41.06252+96-41.06252+47-41.06252+33-41.06252+66-41.06252+27-41.0625216-1=679.2539+896.2539+402.5039+438.3789+122.3789+65.00391+101.2539+24.37891+142.5039+679.2539+903.7539+3018.129+35.2539+65.0039+621.8789+197.878915=8392.937515=559.529167=23.6544≈23.65 Thus, the sample standard deviation is $23.65.c. The degrees of freedom is, df=n-1=16-1=15 The significance level is, 1-α=0.95α=0.05α2=0.0251-α2=0.975 The critical value of χU2 at 15 degrees of freedom can be obtained using the excel function “=CHISQ.INV.RT (0.025, 15)”. The critical value is 27.4884. The critical value of χL2 at 15 degrees of freedom can be obtained using the excel function “=CHISQ.INV.RT (0.975, 15)”. The critical value is 6.2621. The 95% confidence interval of the population standard deviation for the amount adults spend on a Halloween costume is, n-1s2χU2≤σ≤n-1s2χL216-1559.529227.4884≤σ≤16-1559.52926.262117.47≤σ≤36.61 Thus, the 95% confidence interval of the population standard deviation for the amount adults spend on a Halloween costume is $17.47≤σ≤$36.61.