The average of healthy nine year old girl is known to be approximately normally

Question

The average of healthy nine year old girl is known to be approximately normally distributed with a mean of mu = 75 pounds and a standard deviation of sigma = 15 pounds. A complaint is made that the girls living in a local municipal home are A random sample of n = 9 nine year old girls from the home are weighed and found to have a mean weight of x bar = 70 pounds. (a) Formulate the hypotheses to test if the girls in the home are underfed. (b) Calculate the test statistic for this sample. (c) Using the 68-95-99.7 Rule, approximate the p-value. Accompany with an appropriate diagram. (d) Using Stat Crunch, find the test statistic and the p-value. (e) Is the decrease in the girls' weight statistically significant at the alpha = 0.05 level?? (f) Write a short summary of your conclusions, making sure to relate back to the context of the problem.

Explanation / Answer

Solution:-

State the hypotheses. The first step is to state the null hypothesis and an alternative hypothesis.

Null hypothesis: <= 75
Alternative hypothesis: > 75

Note that these hypotheses constitute a one-tailed test. The null hypothesis will be rejected if the sample mean is too small.

Formulate an analysis plan. For this analysis, the significance level is 0.05. 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) = 15 / sqrt(9) = 5
DF = n - 1 = 9 - 1 = 8
t = (x - ) / SE = (70 - 75)/5 = - 1

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.

Here is the logic of the analysis: Given the alternative hypothesis ( > 75), we want to know whether the observed sample mean is big enough to cause us to reject the null hypothesis.

The observed sample mean produced a t statistic test statistic of -1. We use the t Distribution Calculator to find P(t < -1)

The P-Value is 0.173297

Interpret results. Since the P-value (0.173297) is greater than the significance level (0.05), we cannot reject the null hypothesis.

Conclusion. Girls living in municipal children's home are underfed.

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