Question

In a survey conducted by Essential Baby, a random sample of 14 mothers was conducted to estimate the standard deviation of ages, in weeks, at which babies begin to crawl. A normality test of the resulting data is provided below. Use this sample to construct a 95% confidence interval for the standard deviation of the age at which babies begin to crawl.

Summary Statistics

N=14, Mean= 37.214, StDev=9.744, Minimum= 24.000, Maximum=56.000, AD-Value=0.27, and P-value=0.6261

Ho:Data follow a normal distribution

H1: Data do not follow a normal distribution

Conditions: The given sample [a1] (does / does not) appear to have come from a normal distribution. The conditions for constructing the desired confidence interval [a2] (are / are not) satisfied for this sample. The appropriate critical values for the desired interval are χ21-α/2 = [b1] and χ2α/2 = [b2].

Based on the given data, we are 95% confident that the standard deviation of the age at which babies begin to crawl is between [c1] (lower) weeks and [c2] (upper) weeks. (Round your answers to 3 decimal places, if applicable.) Specified Answer for: a1 does not Specified Answer for: a2 are not Specified Answer for: b1 [None Given] Specified Answer for: b2 [None Given] Specified Answer for: c1 [None Given] Specified Answer for: c2 [None Given] Response Feedback: See the ch9formulas handout for formulas for the various CI's, and your lecture notes or the text for examples of calculating them. Make sure you've followed any rounding instructions carefully. Critical value subscripts denote the area to the right of the critical value (even if it's in the left tail) - use this to identify which column each critical value comes from. In calculating the CI bounds, use the sample standard deviation reported by Minitab without rounding this value further. As usual, enter each bound calculation in your calculator in a single step, to avoid further rounding error.

Answer 1

The given sample appears to have come form the normal population since the p-value of the test statistic under the null hypothesis is 0.6261 which is much higher than 0.05. Hence, the null hypothesis may be accepted at 5% level of significance and conclude that the data may have come from the normal population.

The conditions for constructing the desired confidence interval are satisfied for this sample.

The appropriate critical values for the desired confidence interval are:

chi2 1 = 5.008751 and chi2 2 = 24.7356

The confidence interval of the standard deviation is given as:

=(7.064, 15.698) weeks