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.

10.1 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 and the sample standard deviation s. (Round your answers to two decimal places.)

x = mg/dl

s = mg/dl

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

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Answer 1

Here, we have given that,

Xi: calcium level

Xi
10.1
8.8
10.3
9.1
9.4
9.8
10
9.9
11.2
12.1

(A)

Now, we want to find the mean and standard deviation

n= Number of observation =10

= sample mean ==60 mg/dl

S= sample standard deviation= =0.98 mg/dl

(B)

Now, we want to find the 99.9% confidence interval for population mean of total calcium in this patients blood.

Formula is as follows,

Where

E=Margin of error =

Now,

Degrees of freedom = n-1 = 10-1=9

c=confidence level =0.999

=level of significance=1-c=1-0.999=0.001

and we know that confidence interval is always two tailed

t-critical =4.781  ( using t table )

Now,

=

=1.482

We get the 99.9% confidence interval for the population mean

we get the 99.9 % confidence interval

Lower limit= 8.59

Upper limit= 11.55

(C)

Interpretation:

Here, we can say that we are 99.9% confidence that this population mean will fall within this interval.

As mean of average total calcium level below 6 mg/dl for past several months of adult patients is observed for the associated condition but based on the recent data it seems it increased.

that is option 2 is correct

Yes. This confidence interval suggets that the patient no longer has a calcium deficiency