Question

Jennifer Nguyen, a Humber College Healthcare Management program graduate who always had only perfect marks in statistics, was hired by the famous Healthy Lifemedical insurance company. Jennifer is assigned to conduct statistical analysis of medical and financial data. As Jennifer is on probation, please help her to complete the following six tasks. In problems 2-6, state hypotheses H₀and H₁and provide detailed conclusions (based on P-values or critical values/test statistics) together with the Exceloutput. For your convenience the data are given in the Major Assignment Data file. You can also find useful information on the Blackboard in Excel Instructions folder. Jennifer’s manager Dr. Jonathan Steinberg, who has degrees and publications in both mathematical statistics and medical science, asked her to find estimates of the average dental claim reimbursement for 2019. As Healthy Lifehas many thousands of clients it is virtually impossible to calculate the population mean. Using the Excel Random Number Generator function, Jennifer found a random sample of 52 dental claims submitted to Healthy Life. The amounts covered by insurance you can see in the Major Assignment Data file. Please help Jennifer Nguyen to construct90%,95%, and 99%confidence intervals for the true average reimbursement. Make sure that t-distribution is applicable: build a histogram with the bin values, for example, $100, $200, $300, $400, and $500, and check whether it is approximately symmetric and bell-shaped. Then, use Descriptive Statistics function from Data Analysis. Constructing confidence intervals, please round values to two decimal places.

Problem 1.
	Dental Claim Number	Amount Covered		Bin
	1	$192.75		100
	2	$192.75		200
	3	$350.25		300
	4	$200.00		400
	5	$225.00		500
	6	$95.00
	7	$375.50
	8	$380.00
	9	$192.75
	10	$400.00
	11	$230.00
	12	$245.00
	13	$150.00
	14	$250.00
	15	$250.00
	16	$340.00
	17	$225.50
	18	$156.25
	19	$300.00
	20	$350.00
	21	$435.00
	22	$192.75
	23	$192.75
	24	$250.00
	25	$225.00
	26	$230.00
	27	$245.00
	28	$250.00
	29	$250.00
	30	$250.00
	31	$350.00
	32	$98.00
	33	$405.00
	34	$295.00
	35	$205.00
	36	$230.00
	37	$245.00
	38	$750.00
	39	$250.00
	40	$250.00
	41	$340.00
	42	$225.50
	43	$192.75
	44	$192.75
	45	$250.00
	46	$225.00
	47	$350.00
	48	$250.00
	49	$250.00
	50	$340.00
	51	$195.00
	52	$385.00

Answer 1

90% Confidence Interval: 267.216 ± 23.4
(244 to 291)

"With 90% confidence the population mean is between 244 and 291, based on 52 samples."

Short Styles:
267.216 (90% CI 244 to 291)
267.216, 90% CI [244, 291]

Margin of Error: 23.4
(to more digits: 23.38)

Sample Size: 52
Sample Mean: 267.216
Standard Deviation: 102.502
Confidence Level: 90%

95% Confidence Interval: 267.216 ± 27.9
(239 to 295)

"With 95% confidence the population mean is between 239 and 295, based on 52 samples."

Short Styles:
267.216 (95% CI 239 to 295)
267.216, 95% CI [239, 295]

Margin of Error: 27.9
(to more digits: 27.86)

Sample Size: 52
Sample Mean: 267.216
Standard Deviation: 102.502
Confidence Level: 95%

99% Confidence Interval: 267.216 ± 36.6
(231 to 304)

"With 99% confidence the population mean is between 231 and 304, based on 52 samples."

Short Styles:
267.216 (99% CI 231 to 304)
267.216, 99% CI [231, 304]

Margin of Error: 36.6
(to more digits: 36.61)

Sample Size: 52
Sample Mean: 267.216
Standard Deviation: 102.502
Confidence Level: 99%

Histogram:

Size

n =52

sum =13895.25

Mean =x¯ = 267.216346

Median = x~ =250

Mode=250

Standard Deviation

s =102.502882

Variance

s2 =10506.8408

Skewness :

=0.5087

γ1 =2.13349634 >0 implies that given data is approximately symmetric and bell shaped.

Kurtosis :

β2 =11.7677118 >3 this implies given data is leptokurtic