Question

5. The level of calcium in the blood in healthy young adults varies with a mean of about 9.5 mg per liter and standard deviation of about 0.4. A clinic in rural Guatemala measures the blood calcium of 180 healthy pregnant women at their first visit for prenatal care. The mean is 9.58. Is this an indication that the mean calcium level from which these women come is greater than 9.5? (Assume s = 0.4) a. Give a 90% confidence interval for the mean blood calcium level for this population of women and use it to answer the question. I b. What is the margin of error above? C. Approximately how big would our sample need to be for the margin of error to be half as much with 90% confidence? 6. The blood glucose level a person varies throughout the day. Someone with a mean glucose level of more than 200 mg/dL is a diabetic. Diabetes is a serious medical condition and may need to be hospitalized or more extensive care. Sally has not been feeling well and her doctor suspects that she is a diabetic and so sends her home with a blood glucose monitor so that she can test her glucose levels over the course of a week. She was instructed to measure her glucose level 40 times that week. In so doing she found that her average blood glucose level was... a. Set up hypotheses for a significance test to determine if Sally is a diabetic. b. What would a Type I error mean in the context of this problem? c. What would a Type II error mean in the context of this problem? d. If x=205.8 mg/dLand the standard deviation of her measurements was s - 10.6 mg/dl, what is the value of the test statistic that would be used for a significance test?

Answer 1

According to guidelines this is a question with subparts so only first question needs to be answered.

5. Date denote the mean calcium blood ima healthy is notes standard deviation in my/ litre. 9.s adult S = Ho : g.58 M = 9.5 مل 79.5 z 1% -M sis 9 54 11 O-O 29 2.68 32 The two tailed value of a at lol. level significance is 1.645 since calculated value of z is greater than tabulated value 2. (2.68 32 > 1.645) conclude that the calcium level from which these women is are ako tham gos. ( Reject Null Hypothesis) & come DY BUDDIES

. ed = 1.645 using standard Normal Table confidence interval Date women in this population ст TY Z NA S confidence Anterlal - g.58 I 1-645X ory 9. SE 9.5 3.95576 9-623.4424 CI = 9. 539. 63 b) The is E= a boue margin of error s E - 16 45X 1180 0490442 431 o.oug

Hence the margin of error is 0.049.

El2 half of n. = 2 x xo 2 El2 6 4sx ory Date maagin 2 o eror 0 245 7 21.306 721 The required samble s i ze 721