Problem Bank | IB Math AASL

[Maximum mark: 8]

Dr. Alvarez, a nutrition researcher, believes there is an association between a patient’s daily sugar intake, X (in grams), and their fasting blood‑glucose level, Y (in mg/dL). He tests his family and friends and the following paired data points are collected.

Patient	X (g)	Y (mg/dL)
1	50	95
2	60	102
3	70	98
4	80	110
5	90	105
6	100	100
7	110	108
8	120	97
9	130	101
10	140	109
11	150	95
12	160	106

Write down the sampling method used by Dr. Alvarez.
[1]
State one drawback of this sampling method.
[1]
State suitable hypotheses H0 and H1 for a two-tailed test of Dr. Alvarez's claim.
[1]
Carry out the test at the 5% significance level. With reference to the p-value, state your conclusion in the context of Dr. Alvarez's claim.
[4]

Dr. Alvarez fits the regression line of Y on X as Y^=0.50X+80.0.

She uses this to predict that her brother, who consumes 150g of sugar will have a fasting glucose of 155mg/dL.

Comment on the validity of this prediction with a mathematical justificiation.
[1]

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Patient	X (g)	Y (mg/dL)
1	50	95
2	60	102
3	70	98
4	80	110
5	90	105
6	100	100
7	110	108
8	120	97
9	130	101
10	140	109
11	150	95
12	160	106

Patient	X (g)	Y (mg/dL)
1	50	95
2	60	102
3	70	98
4	80	110
5	90	105
6	100	100
7	110	108
8	120	97
9	130	101
10	140	109
11	150	95
12	160	106

Patient	X (g)	Y (mg/dL)
1	50	95
2	60	102
3	70	98
4	80	110
5	90	105
6	100	100
7	110	108
8	120	97
9	130	101
10	140	109
11	150	95
12	160	106

Patient	X (g)	Y (mg/dL)
1	50	95
2	60	102
3	70	98
4	80	110
5	90	105
6	100	100
7	110	108
8	120	97
9	130	101
10	140	109
11	150	95
12	160	106

Patient	X (g)	Y (mg/dL)
1	50	95
2	60	102
3	70	98
4	80	110
5	90	105
6	100	100
7	110	108
8	120	97
9	130	101
10	140	109
11	150	95
12	160	106

Patient	X (g)	Y (mg/dL)
1	50	95
2	60	102
3	70	98
4	80	110
5	90	105
6	100	100
7	110	108
8	120	97
9	130	101
10	140	109
11	150	95
12	160	106