Answer:
The p-value obtained is less than the significance level at which the test was performed, hence, we reject the null hypothesis, accept the alternative hypothesis & conclude that there is evidence showing that the average number of boxes shipped per day is different from 1197.00
Explanation:
For hypothesis testing, we first clearly state our null and alternative hypothesis.
The null hypothesis is that there is no evidence showing that the average number of boxes shipped per day is different from 1197.00. That is, there is no significant difference between the number of boxes shipped per day and 1197.00
And the alternative hypothesis is that there is evidence showing that the average number of boxes shipped per day is different from 1197.00
Mathematically, the null hypothesis is
H₀: μ₀ = 1197.00
The alternative hypothesis is
Hₐ: μ₀ ≠ 1197.00
To do this test, we will use the t-distribution because no information on the population standard deviation is known
So, we compute the t-test statistic
t = (x - μ₀)/σₓ
x = sample mean = 1193.69 boxes per day
μ₀ = standard that we're comparing the sample mean with = 1197.00
σₓ = standard error of the sample mean
= (σ/√n)
where n = Sample size = 24 days
σ = standard deviation of the sample = 3.3166 boxes per day
σₓ = (3.3166/√24) = 0.677
t = (1193.69 - 1197) ÷ 0.677
t = -4.89
checking the tables for the p-value of this t-statistic
Degree of freedom = df = n - 1 = 24 - 1 = 23
Significance level = 0.05
p-value (for t = -4.89, at 0.05 significance level, with a two tailed condition) = 0.000061
The interpretation of p-values is that
When the (p-value > significance level), we fail to reject the null hypothesis and when the (p-value < significance level), we reject the null hypothesis and accept the alternative hypothesis.
So, for this question, significance level = 5% = 0.05
p-value = 0.000061
0.000061 < 0.05
Hence,
p-value < significance level
This means that we reject the null hypothesis, accept the alternative hypothesis & conclude that there is evidence showing that the average number of boxes shipped per day is different from 1197.00
Hope this Helps!!!