Question

Use the dataset “ChickWeight”, available in R. Assume that each row is an observation of a unique chick. weight is the weight of the chick. Diet is the diet treatment that the chick received. Assume that the distribution of chickweigts within each diet is approximately normal and variances are equal.

1. Construct a 95% confidence interval for the true mean weight of chicks.

2. Interpret the confidence interval in 1. in the context of the problem.

3. Construct a 99% confidence interval for the true mean weight of chicks.

4. Interpret the confidence interval in 2. in the context of the problem.

5. Write down the null and alternative hypothesis to determine if the mean weight of chicks is greater than 120.

6. Conduct a statistical test to determine if the mean weight of chicks is greater than 120. Use = 0.05.

7. Construct a box-and-whisker plot of weight by Diet. Label the graph and axes appropriately. (Hint: there should be 4 box-and whisker plots on one graph)

8. Write down the null and alternative hypothesis to determine if there is a difference in mean weight between diets.

9. Use an ANOVA to determine if there is a difference in mean weights between diets. Assume that all of the assumptions are met to perform the procedure. = 0.05.

10. If there is a difference in mean weights between diets, use a statistical procedure to rank the means where possible.

Answer 1

Solution1:

Rcode:

attach(ChickWeight)

dim(ChickWeight)
data(ChickWeight)
t.test(ChickWeight$weight)

output:

One Sample t-test

data: ChickWeight$weight
t = 41.208, df = 577, p-value < 2.2e-16
alternative hypothesis: true mean is not equal to 0
95 percent confidence interval:
116.0121 127.6246
sample estimates:
mean of x
121.8183

95 percent confidence interval lies in between  116.0121 and
127.6246.

2. Interpret the confidence interval in 1. in the context of the problem.

we are 95% confident that the true mean weight of chicks lies in between 16.0121 and
127.6246.

3. Construct a 99% confidence interval for the true mean weight of chicks.

Rcode:

t.test(ChickWeight$weight,conf.level = 0.99)

output:

One Sample t-test

data: ChickWeight$weight
t = 41.208, df = 577, p-value < 2.2e-16
alternative hypothesis: true mean is not equal to 0
99 percent confidence interval:
114.1784 129.4583
sample estimates:
mean of x
121.8183

. Interpret the confidence interval in 2. in the context of the problem.

we are 99% confident that the true mean weight of chicks lies in between  114.1784 and 129.4583

Solution5:

5. Write down the null and alternative hypothesis to determine if the mean weight of chicks is greater than 120.

H0:

Ha: