R Notebook

Hw#6

#Question7

k <- qt(0.9, df = 6)
k

[1] 1.439756

#Question8

P_Z_gt_2 = pnorm(2, lower.tail = FALSE)

P_T_gt_2_df40 = pt(2, df = 40, lower.tail = FALSE)
P_T_gt_2_df20 = pt(2, df = 20, lower.tail = FALSE)
P_T_gt_2_df10 = pt(2, df = 10, lower.tail = FALSE)
P_T_gt_2_df5  = pt(2, df = 5,  lower.tail = FALSE)

#As degrees of freedom increase:
#The t-distribution gets closer to the standard normal.
#The tail probabilities like P(T>2) decrease.

#Question9

k <- qt(0.995, df = 19)
k

[1] 2.860935

#Question10

data(morley)

speed = morley$Speed
adjusted_speed = speed + 299000
x_bar = mean(adjusted_speed)
s = sd(adjusted_speed)
n = length(adjusted_speed)

df = n - 1

t_crit = qt(0.975, df = df)

margin = t_crit * (s / sqrt(n))

lower = x_bar - margin
upper = x_bar + margin

cat("95% Confidence Interval for the speed of light (km/s):\n")

95% Confidence Interval for the speed of light (km/s):

cat(round(lower, 2), "to", round(upper, 2), "\n")

299836.7 to 299868.1