As part of a study of the development of the thymus gland, researchers weighed the glands of five chick embryos after 14 days of incubation. The thymus weights mean is 31.7 mg and the standard deviation is 8.7 mg. Using a significance level of 0.10, complete the following:

a) What is the value of 0

b) What is the sign of the alternative hypothesis (answer with either: less/greater/not equal)?

c) Is this a Z or T test (answer with: Z or T)?

d) What is the value of the test statistic to 4 decimal places?

e) If you could draw the p-value region, how many sides would you shade (answer with: 1 or 2)?

f) Using R (you do not need to enter the command), what is the p-value to 4 decimal places (you may need to use scientific notation as some p-values are small such as 1.0423E-7 would be acceptable)?

g) Do you reject or fail to reject the null hypothesis (answer with: reject/fail to reject)?

h) What is the contextual (the rest of the madlib/conclusion) conclusion? For example, we have enough evidence to .....

i) Make a 90% confidence interval for the true mean weight of the thymus gland. (enter the answer as (lower bound, upper bound) to 4 decimal places and units.

j) Does the confidence interval support the true mean weight can be 35 mg? Yes or no and why?

k) Does the result of the hypothesis test you conducted match the result of the confidence interval you created? Yes or no and why?