1. Assuming that the total charges variable in the Patients dataset is normally distributed, use a one-tail t-test of hypothesis ( = 0.05) for the

1. Assuming that the total charges variable in the Patients dataset is normally distributed, use a one-tail t-test of hypothesis (α = 0.05) for the mean (σ unknown) to test the hypothesis that the population mean total charges is greater than $10,000.

2. Using the pooled variance t-test for the difference between two means, at the 0.05 level of significance, is there evidence that the mean age for male patients is different from the mean age for female patients? Be sure to provide the null and alternate hypotheses.

Length of Stay	Age (Years)	Sex (M/F/U)	Total Charges
3	78	F	$5,418.85
3	74	F	$4,575.10
11	89	M	$12,031.18
3	81	M	$3,617.84
9	87	F	$12,806.88
3	65		$5,295.55
3	90	M	$3,453.21
3	61	M	$1,760.03
3	90	F	$3,290.40
5	78	M	$6,253.65
3	78	F	$3,896.16
2	71	M	$1,795.35
3	76	M	$9,265.17
3	76	F	$3,282.90
5	79	F	$9,565.83
3	72	M	$3,782.15
4	72	M	$6,384.28
3	64	M	$4,904.25
2	72	F	$4,169.92
3	69	F	$5,204.41
4	63	M	$6,740.00
1	78	M	$5,016.44
2	83	M	$4,178.94
3	62	F	$4,105.26
4	71	M	$4,717.30
6	83	F	$6,598.92
2	63	F	$1,633.85
1	83	M	$2,200.85
4	76	F	$7,461.54
5	79	M	$11,413.23
3	65	M	$5,607.55
2	79	M	$4,850.62
4	74	M	$7,102.49
15	63	M	$13,615.69
3	84	M	$5,069.18
6	90	F	$6,536.07
4	73	F	$7,401.25
2	81	M	$3,744.34
5	75	F	$8,653.68
9	87	F	$14,423.21
3	70	M	$3,742.30
3	73	F	$5,514.09
5	77	M	$7,390.15
5	71	M	$9,358.20
7	76	M	$14,570.29
4	49	F	$4,526.43
6	78	F	$6,846.77
2	86	M	$2,927.62
3	67	M	$4,404.13
6	69	M	$8,056.36
8	73	F	$10,703.34
4	88	F	$16,458.95
5	67	M	$4,770.10
8	69	M	$15,282.57
7	77	M	$10,105.30
8	64	F	$7,871.29
3	76	M	$3,411.10
12	64	F	$10,962.17
2	41	M	$7,374.27
5	49	M	$7,788.51
5	59	M	$8,191.10
3	81	M	$11,117.35
2	74	F	$5,624.54
4	77	F	$4,574.92
3	78	F	$3,644.36
2	73	F	$2,937.92
6	67	M	$3,944.78
3	80	M	$6,366.10
3	77	F	$4,992.01
4	73	F	$6,929.35
5	67	M	$5,595.42
3	86	M	$3,466.70
7	82	F	$7,289.77
7	84	F	$6,375.95
3	73	F	$3,585.62
4	82	M	$5,970.45
8	62	F	$10,578.14
2	84	M	$2,223.60
3	89	F	$2,250.50
1	84	M	$1,644.55
4	81	F	$2,491.45
3	81	F	$1,691.50
6	78	M	$7,931.92
5	84	F	$5,121.97
5	37	M	$6,940.75
7	62	M	$12,088.08
1	80	F	$2,325.60
2	80	F	$4,452.78
4	73	M	$6,157.43
11	80	F	$21,474.90
3	80	F	$8,566.51
2	80	F	$4,910.27
1	81	F	$3,275.03
4	39	M	$12,080.81
6	86	M	$7,436.85
8	79	M	$15,624.20
4	87	M	$4,590.48
2	53	F	$3,232.63
3	83	F	$3,768.11
7	80	F	$9,862.26
7	79	F	$10,626.42
4	72	F	$6,967.99
3	77	F	$5,891.25
3	81	F	$4,756.91
9	67	F	$8,096.93
4	80	M	$4,620.59
6	67	F	$5,796.49
1	88	M	$1,483.39
1	88	F	$2,510.05
6	92	F	$10,185.83
3	85	F	$3,391.90
5	85	M	$8,418.13
3	80	M	$4,346.47
2	98	F	$2,043.85
3	74	F	$2,594.85
5	77	M	$5,499.36
9	53	F	$11,244.45
7	93	M	$6,565.55
4	83	F	$6,031.15
7	80	M	$4,912.76
3	79	M	$6,182.45
3	87	F	$4,218.95
16	59	M	$40,231.27
3	81	F	$3,608.95
4	94	F	$3,041.44
1	33	F	$1,581.93
2	78	F	$1,468.48
2	29	F	$2,294.55
2	80	F	$7,138.72
3	63	F	$3,845.96
4	86	M	$5,355.23
4	96	M	$4,573.05
5	89	M	$5,023.11
5	80	M	$4,238.30
5	55	F	$6,885.73
5	73	M	$5,447.63
7	67	F	$6,257.66
2	75	M	$4,601.00