The level of calcium in the blood of healthy young adults follows a normal distr
ID: 3295689 • Letter: T
Question
The level of calcium in the blood of healthy young adults follows a normal distribution with mean = 10 milligrams per deciliter and standard deviation = 1.0. A clinic measures the blood calcium of 100 healthy pregnant young women at their first visit for prenatal care. The mean of these 100 measurements is x = 9.8. Is this evidence that the mean calcium level in the population from which these women come is less than 10?
a. State the hypotheses you will test.
b. Calculate the test statistic.
c. State the distribution of the test statistic.
d. Find the p-value.
e. State your conclusions.
Explanation / Answer
Solution:-
State the hypotheses. The first step is to state the null hypothesis and an alternative hypothesis.
Null hypothesis: > 10
Alternative hypothesis: < 10
Note that these hypotheses constitute a one-tailed test.
Formulate an analysis plan. For this analysis, the significance level is 0.01. The test method is a one-sample t-test.
Analyze sample data. Using sample data, we compute the standard error (SE), degrees of freedom (DF), and the t statistic test statistic (t).
SE = s / sqrt(n)
S.E = 0.1
DF = n - 1 = 100 - 1
D.F = 99
t = (x - ) / SE
t = - 2
where s is the standard deviation of the sample, x is the sample mean, is the hypothesized population mean, and n is the sample size.
The observed sample mean produced a t statistic test statistic of - 2.0. We use the t Distribution Calculator to find P(t < - 2) = 0.024
Thus the P-value in this analysis is 0.024
Interpret results. Since the P-value (0.024) is greater than the significance level (0.01), we cannot reject the null hypothesis.
From the above test we do not have sufficient evidence in the favor of the claim that the mean calcium level in the population from which these women come is less than 10.
Related Questions
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.