Please answer the questions below using $R$ notebook and $R$ markdown, with each answer placed

within a chunk. Specify which question each chunk corresponds to above it$,$ and make sure to

include your name and student ID in the author section above. You are required to use Knit render

to upload your answers in HTML format to the assignment section in the MS TEAMS channel.

Assignments not in HTML format will not be accepted. The use of codes not demonstrated or

utilized in class will result in a reduction of the score for that question. Additionally, the incorrect

application of statistical analyses or tests will lead to a deduction of points for the related question.

Furthermore, any attempt at plagiarism will result in an automatic grade of zero for the homework.

Best of luck.

Question $1$

Using the Palmer Penguins dataset, calculate the $90\%$ confidence interval for the mean flipper

length of the penguins. Assume that the flipper lengths are normally distributed. $(30$ pts$.)$

Question $2$

Using the Palmer Penguins dataset, perform a one$-$sample t$-$test to determine if the mean bill

length of male Adelie penguins on Biscoe Island is significantly different from $40mm.$ Assume a

significance level of $0\mathrm{.}05.(40$ pts$.)$

Question $3$

You have been given the Palmer Penguins dataset. Your task is to determine if there is a

significant difference in the mean bill depth between female Adelie penguins and female Gentoo

penguins. Assume a significance level of $0\mathrm{.}05.(40$ pts$.)$