Problem

A concern to public health officials is whether a concentration of lead in the paint of older homes may have an effect on the muscular development of young children. In order to evaluate this phenomenon, a researcher exposed 90 newly born mice to paint containing a specified amount of lead. The number of Type 2 fibers in the skeletal muscle was determined 6 weeks after exposure. The mean number of Type 2 fibers in the skeletal muscles of normal mice of this age is 21.7. The n = 90 mice yielded  Is there significant evidence in the data to support the hypothesis that the mean number of Type 2 fibers is different from 21.7 using an α = .05 test?

Step-by-step solution

1. Step 1 of 3

   From the information, observe that a concern to public health officials is whether a concentration of lead in the patient of older homes may have an effect on the muscular development of the younger child.

   Consider a random sample of 90 newly born mice with mean 18.8 and sample standard deviation of 15.3

   The summary statistics as follows:

   Sample mean, 

   Sample standard deviation, 

   Sample size, 

   Consider Null and Alternative hypothesis.

   Null hypothesis, the mean number of type-II fibres is not differ from 21.7

   That is, 

   Alternative hypothesis,  the mean number of type-II fibres is differ from 21.7

   That is, 

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2. Step 2 of 3

   Calculate the test statistic value as follows:

   

   Calculate the degree of freedom as follows:

   

   The critical value of t for 5% level of significance and 89 degree of freedom is 1.99

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3. Step 3 of 3

   Compare the calculated value with the critical value.

   If calculated value exceeds the critical value then reject the Null hypothesis.

   Here, the calculated value lesser than the critical value then fail to reject the Null hypothesis.

   Hence, conclude that the mean number of type-II fibres is not differ from 21.7

   Comment