Question

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. 9.1 8.8 10.3 9.1 9.4 9.8 10.0 9.9 11.2 12.1 (a) Use a calculator with mean and sample standard deviation keys to find the sample mean reading x bar and the sample standard deviation s. (in mg/dl; round your answers to two decimal places.) x bar = mg/dl s = mg/dl (b) Find a 99.9% confidence interval for the population mean of total calcium in this patient's blood. (in mg/dl; round your answer to two decimal places.) lower limit mg/dl upper limit mg/dl (c) Based on your results in part (b), do you think this patient still has a calcium deficiency? Explain. Yes. This confidence interval suggests that the patient may still have a calcium deficiency. Yes. This confidence interval suggests that the patient no longer has a calcium deficiency. No. This confidence interval suggests that the patient may still have a calcium deficiency. No. This confidence interval suggests that the patient no longer has a calcium deficiency.

Answer 1

WE WILL BE USING R STUDIO FOR CALCULATING THE 99.9% CONFIDENCE INTERVAL . ALL CODES

ARE MARKED IN BLACK

# Input of data values as vectors
# x= total calcium level
x <- c(9.1, 8.8, 10.3, 9.1, 9.4, 9.8, 10.0, 9.9, 11.2, 12.1)
n <- length(x)
# x_bar = mean
x_bar <- mean(x)
# s = sd of x
s <- sd(x)
# ci = confidence interval
ci <- 0.999
# lcl=lower limt
lcl <- x_bar-abs(qt(0.5*(1-ci),n-1,lower.tail = TRUE))*s/(sqrt(n))
ucl <- x_bar+abs(qt(0.5*(1-ci),n-1,lower.tail = TRUE))*s/(sqrt(n))
print(lcl)
print(ucl)

The 99.9% confidence interval is

{ 8.424829, 11.51517}

Inference

Since our confidence does not contain 6 mg/dl and our confidence is more than this hence

No. This confidence interval suggests that the patient no longer has a calcium deficiency.