### Calculate a 95 confidence interval for the unknown

**Question 1:**

Total blood volume (in mL) per body weight (in kg) is important in medical research. Results of the red blood cell volume can indicate a medical problem. From a series of red blood volume test results, seven results were randomly selected for a subject. Assume that the sample comes from a population that follows a normal distribution. The data can be found in the Excel file: Ass_2 on Blackboard.

(a) Calculate a 95% confidence interval for the unknown population mean of red blood cell volume.

(b) It was stated that the population mean of red blood cell volume is 28 mL/kg. Is the test results different from the stated value? Test this claim at a 5% significant level.

**Question 2:**

It is believed that regular physical exercise leads to a lower resting pulse rate. A random sample of 20 subjects had their resting pulse rate measured and asked whether they regularly exercised or not. Assume that this sample is from a population that follows a normal distribution.

A claim was made that there is a difference in resting pulse rates between those who exercise regularly and those who do not exercise regularly. Test this claim at a 5% level of significance. The data can be found in the Excel file: Ass_2 on Blackboard.

**Question 3:**

Dual-energy X-ray absorptiometry (DXA) is a technique for measuring bone health. One of the most common measures is total body bone mineral density (TBBMD). A highly skilled operator is required to take the measurements.

Recently, a new DXA machine was purchased by a laboratory, and two operators were trained to take the measurements. TBBMD for randomly selected eight patients was measured by both operators. The units are in grams per centimetre squared (g/cm2). A comparison of the means for the two operators provides a check on the training they received and allows us to determine if one of the operators is producing measurements that are higher than the other operator. Assume that the samples come from a population that follows a normal distribution. The data can be found in the Excel file: Ass_2 on Blackboard.

(a) The laboratory wants to test if there is a difference between the two operators. Test this claim at a 5% significant level.

(b) The laboratory is interested in the range of differences that would be compatible with the data. Calculate a 95% confidence interval to give the range of these differences.

**Attachment:-** Assignment.rar

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