(Solved): Confidence Intervals Project Module 7: Confidence Intervals in Excel Use the Excel file provided to ...

Confidence Intervals Project Module 7: Confidence Intervals in Excel Use the Excel file provided to perform the calculations and provide necessary answers. Question 1 The Specific Absorption Rate (SAR) for a cell phone measures the amount of radio frequency (RF) energy absorbed by the user's body when using the handset. Every cell phone emits RF energy. Different phone models have different SAR measures. To recelve certifcation from the Federal Communications Commission (FCC) for sale in the United States, the SAR level for a cell phone must be no more than 1.6 watts per kilogram. The table in the Excel file (also in our book and notes) shows the highest SAR level for a random selection of cell phone modeis as measured by the FCC. Find a \$98$ confidence interval for the true (population) mean of the Specific Absorption Rates (SARs) for cell phones. Assume \\( \\sigma=0.337 \\). a) [0.5] L2: Use Art of Stat to find the confidence interval. Go to the Normal Distribution App > Find Percentile/Quantile; enter the sample mean and the standard error that represent the distribution of the sample means; selected Two-Talled percentile and set central probability to \$98$. Take a screenshot of the input and output windows and insert in your spreadsheet. Resize the image to fit the given area. b) \\( [1.0] \\) E2: Use the COUNT function in excel to calculate the sample size E3: Use the AVERAGE function in excel to calculate the sample mean E4: Enter the population standard deviation E5: Enter the confidence level in percent form E7: Use the confidence level in E5 to calculate alpha \\( (a=1-C L) \\) E8: Use the value of alpha in E7 to calculate alpha-half (the area in each tail) G3: Copy the value of the sample size (from E2 - do not enter the value yourself) H3: Copy the value of the sample mean (from E3) 13: Copy the value of the standard deviation (from E4) c) [1.0] G7: Copy the value of the point estimate for the population mean (no manual entries) H7: Use the formula for the standard error of the sample means to calculate the value of the standard error. Use variable locations and not values: \\( \\sigma_{x}=\\frac{\\sigma}{\\sqrt{n}} \\) 17: Calculate \\( z_{a / 2} \\) using the inverse standard normal function NORM.S.INV with probability equal to the percentile of the right tail \\( \\left(1-\\frac{a}{2}\\right) \\). Use variable locations. D14:Explain why in the previous step we do not use \\( \\frac{a}{2} \\) as the probablity of the inverse normal function to find the z-score 17: Calculate the Margin of Error (EBM - Error Bound for Moan) as EBM \\( =z_{a / 2} \\cdot \\sigma_{x} \\) d) [1.0] G11:Type the symbol for the population parameter we are trying to estimate. H11:Calculate the lower bound of the confidence interval as (point_estimate - EBM) (use locations of variables) 111: Calculate the upper bound of the confidence interval as (point_estimate + EBM) (use locations of variables) J11: Copy the confidence level from E5. o) [0.5] D21:Interpret the confidence interval using complete sentences.\r\n\r\n\r\nQuestion 2 You do a study of hypnotherapy to determine how eflective it is in increasing the number of hours of sleep each night for adults 45 years old or older. You measure hours of sleep for 12 adults in that age range with the following results: 8.29 .1 7.7.8.6 \\( 6.9 \\quad 11.2 \\quad 10.19 .9 \\quad 8.9 \\quad 9.2 \\quad 7.5 \\quad 10.5 \\) Construct a \$95$ confidence interval for the mean number of hours slept for the population (assumed normal) from which you took the data. a) [0.5] L36: Find the confidence interval in Art of Stat. Go to the Inference for a Population Mean App > Confidence Interval \\& Significance Test; Enter Data: Your Own (select from menu); Name of Variable: Sleep Time (type it in); Observations: copy the data from cell A50 into that box (they are already separated by spaces as required); Type of Inference: Confidence Interval; Confidence Level: \$95$ (slider). Make sure Interval is selected for interval, Lower or Upper Bound? Take a screenshot of the input and output windows and insert in your spreadsheet. Resize the image to fit the given area. b) [0.5] E36: Use the COUNT function in excel to calculate the sample size E37: Use the AVERAGE function in excel to calculate the sample mean E38: Use the STDEV.S function in excel to calculate the sample standard deviation E39: Enter the confidence level in percent form E41: Use the confidence level in E39 to calculate alpha \\( (\\alpha=1-C L) \\) E42: Use the value of alpha in E41 to calculate alpha-half (the area in each tail) G37: Copy the value of the sample size (from E36 - do not enter the value yourself) H37: Copy the value of the sample mean (from E37) 137: Copy the value of the standard deviation (from E38) c) [1.0] J37: Calculate the degrees of freedom \\( (d f=n-1) \\) using location G37 for \\( n \\) G42: Copy the value of the point estimate for the population mean (no manual entries) H42: Use the formula for the standard error of the sample means to calculate the value of the standard error. Use variable locations and not values: \\( s_{x}=\\frac{z}{\\sqrt{11}} \\) 142: Calculate \\( t_{i d / 2} \\) using the inverse-T-2tail function T.INV.2T with probability equal to alpha and degrees of freedom found in J37. Use variable locations. D48: Explain why in the previous step the function T.INV.2T gives us \\( t_{\\alpha / 2} \\) when we enter probablity equal to \\( \\alpha \\). J42: Calculate the Margin of Error (EBM - Error Bound for Mean) as EBM \\( =t_{a / 2} \\cdot s_{x} \\) d) [0.5] G45: Type the symbol for the population parameter we are trying to estimate. H45: Calculate the lower bound of the confidence interval as (point_estimate-EBM) (use locations of variables) 145: Calculate the upper bound of the confidence interval as (point_estimate + EBM) (use locations of variables). Make sure the interval in Art of Stat agrees with the one you calculated in Excel. 145: Copy the confidence level from E39. e) \\( [0.5] \\) D55: Interpret the confidence interval using complete sentences.\r\nQuestion 3 For a class project a polical science student at a large univenty wands le estimate the percent of studerts whe are regivered voter. He survers 500 students and finds that 321 are registerpd volers. LCENSES AND ATTRIBUTIONS co ucensto contont, oficand. Compute a ros confidence interval for the true percent of students who are regialared veterk, and interpot the confidence interval a) 10.5, L70. Find the confidence interval in Avt of Stot. Co to the inference for a Population Proportion App > Confidence Interval S Significance Test Enter Oata: Number of Successes (select from menu); type in the Sample Sure and \\( = \\) of Successes: Type of Inference: Confidence Intervat; Confidence Level \$90$ (slider). Make wro interval is selected for Interval, Lower or Upper Bound? Under Options, select Show z-score for Margin of Erroe. Take a screenshot of the input and oulput windows and insert in your spreadsheet. Resice the image to fit the area. b) [0.5] E70: Enter the sarrole size E71: Enter the \"number of successes\" (number of studenss who are registered) E72 Enter the confidence level in percent form E74: Use the confidence level in E72 to calculate alpha \\( (a=1-C l) \\) E75. Use the value of alpha in E74 to calculate alpha-half (the area in eachtai) E78: Calculate the proportion of registered voters in the sample: \\( p=\\frac{z}{*} \\), use locations E79. Calculate the proportion of students not regatered: a \\( =1-\\$ \\); use locations G71: Copy the value of the sample sizo (from E70 - do not enter the value yoursel) H71: Copy the number of successes (from E71) I71: Copy the sample proportion you calculated (from E78) c) \\( [0.51 \\quad \\mathrm{~A} 73 \\) : State the two conditions that must apply in order fo use confidence interval for the true population proportion estimation B77: Calculate the quantly \\( n \\cdot \\dot{p} \\) using Excel variable locations B78: Calculate the quantiy \\( n \\cdot 4 \\) using Excel variabie locations A83: Based on your calculations above, can confidence interval be used in this case to eatmate the the population proportion of registered cellege students? Explain. d) 10.5\\( ] \\) G75: Copy the value of the point eatimate for the population proportion (use locationa). H75: Use the formula for the standard error of the sample proportion to calculate the value of the standard error. Use variable locations and not values: \\( x_{y}=\\sqrt{\\frac{4}{m}} \\) 175: Calculate \\( x_{2 / 2} \\) using the inverso standard normal function NORM.S INV wich probablify equal to the percentile of the right tal \\( \\left(1-\\frac{5}{2}\\right) \\). Use variable locations. DB2. Explain why in the previous step wo do not use \\( \\frac{1}{2} \\) as the probabaly of the imverse normal function to find the z-score. J75. Calculate Margin of Error (EBP - Error Bound for Proportion) as EBP = \\( z_{* / 2} * x \\). o) 10.5\\( ) \\mathrm{G} 9 \\) : Type the symbol for the population parameter we are tying to easimate. H79: Calculate the lower bound of the conkidence interval as (point_ostimate - EEP) (use locations of variables) 179. Calculate the upper bound of the confidence interval as (point estimate + EBP) (Use locations of variables). Make sure the interval in Avt of Stat agrees with the one you calculated in Excel 79. Copy the confidence level from E72 1) \\( [0.5] \\) D8. Interpret the confidence interval using complete sentences: