Question

Use R.  Provide Solution and R Code within each problem.

A study was conducted to determine the average weight of newborn babies. The distribution of the weight of newborn babies has a standard deviation of σ = 1.25lbs. A random sample of 100 newborn babies was taken and weights measured. The mean weight of the babies in the sample was 7.3 lbs.

a. Construct a 95% confidence interval for the true mean weight of newborn babies.

b. Interpret the confidence interval in a.

c. Write the null and alternative hypotheses to determine if the true mean weight of newborn babies is less than 7.75 lbs.

d. Conduct a statistical test to determine if the true mean weight of newborn babies is less than 7.75 lbs.

i. Pvalue

ii. Conclusion

Answer 1

(a)

Following is the R code

Following is the output generated by R:

Answer (7.055, 7.545)

(b)

We are 95% confident that true mean weight og newborn babies is lie in the above interval.

(c)

Hypotheses are:

(d)

Following is the screen shot of r script:

Following is the output generated by R:

i. P-value = 0.0002

ii. Conclusion: Since p-value is less than 0.05 so we reject the null hypothesis. There is evidence to conclude that the true mean weight of newborn babies is less than 7.75 lbs.