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eburnhisel2023
09.11.2019 •
Mathematics
Wo machines used to fill soft drink containers are being compared. the number of containers filledeach minute is counted for 60 minutes for each machine. during the 60 minutes, machine 1 filledan average of 73.8 cans per minute with a standard deviation of 5.2 cans per minute, and machine2 filled an average of 76.1 cans per minute with a standard deviation of 4.1 cans per minute.(a) we want to test whether machine 2 is faster than machine 1. state the null and alternatehypotheses.(b) compute the relevant statistic.(c) compute the p-value.
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Ответ:
a) The null hypothesis is H₀ : µ₁ ≥ µ₂
The alternative hypothesis is Hₐ : µ₁ ≤ µ₂ (left tailed)
b) using t-test, t= -2.69
c) the p-value = 0.0041
Step-by-step explanation:
Testing if the machine 2 is faster than the machine 1 is tested under the null and alternative hypothesis at a 5% level of significance.
For machine 1
Mean (µ₁)= 73.8
Standard deviation (σ₁) = 5.2
n₁ = 60
For machine 2
Mean (µ₂)= 76.1
Standard deviation (σ₂) = 541
n₂ = 60
a) The null hypothesis is H₀ : µ₁ ≥ µ₂
The alternative hypothesis is Hₐ : µ₁ ≤ µ₂ (left tailed)
b) Using t-test
t = (µ₁ - µ₂) / √ (σ₁^2/ n₁) + (σ₂^2/ n₂)
t= (73.8 – 76.1) / √ (5.2^2/ 60 )+ (4.1^2/ 60)
t= (-2.31) / √0.7309
t= -2.31/ 0.8549
t= -2.69
c) The excel function for the p-value = TDIST (2.69, 118, 1)
P-value = 0.0041
Since the p-value is less than the 5% significance level, we reject the null hypothesis.
The then conclude that machine 2 is faster than machine 1
Ответ:
Step-by-step explanation:
1. Put them in order from least to greatest first
33, 64, 71, 73, 78, 79, 81, 81, 83, 83, 85, 85, 86, 88, 93, 95, 97, 97, 99, 100
2. Mean
Add them all, the divide the sum by the total number of grades
33+64+71+73+78+79+81+81+83+83+85+85+86+88+93+95+97+97+99+100= 1566
1566/20= 78.3
3. Median
Find the number in the middle, if there's two, add them and divide by two
83+85= 168
168/2= 84
4. Mode
Find the numbers that reoccurs the most
81, 83, 85, 97