數學問題~ 請進 help2

1.16 mean 1.182352941
1.18 standard deviation 0.021368614
1.21
1.16
1.22
1.2
1.14
1.18
1.17
1.18
1.21
1.18
1.17
1.19
1.2
1.16
1.19
(a)
We need to use t-distribution since the sample size is less than 30. The underlying theory assumes normally distributed data, i.e. that the individual observations are independent and identically distributed observations from a normal distribution with mean μ and unknown variance σ^2.
(b)
μ = 1.1824 Standard deviation, σ= 0.02137
a 95% confidence interval estimate for the true average weight of the birthday cake
=(1.1824-2.12 (0.02137/√17), 1.1824+2.12 (0.02137/√17))
=(1.17,1.19)
(c)
H0: μ>=1.2
H1: μ<1.2
alpha=5%, Critical value=1.746
Test-statistic
=(1.1824-1.2)/ (0.02137/√17)
=-3.39573
Since |Test-statistic|>1.746, reject H0 and conclude that there is enough evidence to infer that the birthday cake is underweight
(d)
The p-value of Test-statistic=-3.39573 is around 1-0.9981=0.0019
Since 0.0019<0.05 reject H0 and conclude that there is enough evidence to infer that the birthday cake is underweight

a1.16 b1.18 c1.21 d1.16