Over the past several months, an adult patient has been treated for tetany (severe muscle spasms). This condition is associated with an average total calcium level below 6 mg/dl. Recently, the patient's total calcium tests gave the following readings (in mg/dl). Assume that the population of x values has an approximately normal distribution.

9.40

8.70

10.20

9.00

9.40

9.80

10.00

9.90

11.20

12.10

(a)

Use a calculator with mean and sample standard deviation keys to find the sample mean reading x and the sample standard deviation s.

(b)

Find a 99.9% confidence interval for the population mean of total calcium in this patient's blood.

(c)

Based on your results in part (b), do you think this patient still has a calcium deficiency? Explain.

A study of parental empathy for sensitivity cues and baby temperament (higher scores mean more empathy) was performed. Let x₁ be a random variable that represents the score of a mother on an empathy test (as regards her baby). Let x₂ be the empathy score of a father. A random sample of 38 mothers gave a sample mean of x₁ = 69.55. Another random sample of 31 fathers gave x₂ = 59.89. Assume that ₁ = 11.48 and ₂ = 11.37.(a)Let ₁ be the population mean of x₁ and let ₂ be the population mean of x₂. Find a 99% confidence interval for ₁ - ₂.(b)Examine the confidence interval and explain what it means in the context of this problem. Does the confidence interval contain all positive, all negative, or both positive and negative numbers? What does this tell you about the relationship between average empathy scores for mothers compared with those for fathers at the 99% confidence level?