Solution:
Here, we have to use one sample t test for the population mean.
The null and alternative hypotheses are given as below:
H0: µ = 5 versus Ha: µ > 5
This is an upper tailed test.
The test statistic formula is given as below:
t = (Xbar - µ)/[S/sqrt(n)]
From given data, we have
µ = 5
Xbar = 6.7
S = 2.37
n = 25
t = (Xbar - µ)/[S/sqrt(n)]
t = (6.7 - 5)/[2.37/sqrt(25)]
t = 3.5865
df = n – 1 = 25 - 1 = 24
α = 0.01
Critical value = 2.4922
(by using t-table or excel)
P-value = 0.0007
(by using t-table)
P-value < α = 0.01
So, we reject the null hypothesis
There is sufficient evidence to conclude that the mean weight is larger than 5 kg at a level of significance of 1%.
So, given statement is False.
Answer: False
An engineer measures the weights (in kilograms) of steel pieces. They would like to test H:...
An engineer measures the weights (in kilograms) of steel pieces. They would like to test H0 : = 5 against H1 : > 5. The weight of a steel piece is normally distributed. They select a random sample size of n = 25 steel pieces, and compute x = 6:7 and s = 2:37. We cannot conclude that the mean weight is larger than 5 kg at a level of significance of 1%. True False An engineer measures the weights...
An engineer measures the weights (in kilograms) of steel pieces. They would like to test Ho : 4 = 5 against H : H > 5. The weights follow a normal distribution with variance 16. Using a sample of size n = 25, the engineer decides to reject H, if T > 6. Assuming that the true population mean is 5.2, determine the probability of committing an error of Type II error. A. 0.8413 B. 0.05 C. 0.9332 D. 0.8943...
An engineer measures the weights (in kilograms) of steel pieces. They would like to test H0 : µ = 5 against H1 : µ > 5. The weights follow a normal distribution with variance 16. Using a sample of size n = 25, the engineer decides to reject H0 if x > 6. Assuming that the true population mean is 5.2, determine the probability of committing an error of Type II error.
An engineer measures the weights (in kilograms) of steel pieces. They would like to test H0: μ= 5 against 1: μ >5. The weights follow a normal distribution with variance 16. Using a sample of size n= 25, the engineer decides to reject H0 if x >6. Assuming That the true population mean is 5.2, determine the probability of committing an errorof Type II error. A. 0.8413 B. 0.05 C. 0.9332 D. 0.8943 E. none of the preceding
Multiple Choice Question An engineer measures the weights (in kilograms) of steel pieces. They would like to test Ho : H = 5 against H:4 > 5. The weights follow a normal distribution with variance 16. Using a sample of size n= 25, the engineer decides to reject H, if I > 6. Determine the probability of committing an error of Type I error. A. 0.0500 B. 0.1057 C. 0.8943 D. 0.1000 E. none of the preceding
Multiple Choice Question An engineer measures the weights (in kilograms) of steel pieces. They would like to test Ho : u = 5 against H1: u > 5. The weights follow a normal distribution with variance 16. Using a sample of size n = 25, the engineer decides to reject H, if 7 > 6. Assuming that the true population mean is 5.2, determine the probability of committing an error of Type II error. A. 0.8413 B. 0.05 C. 0.9332...
13. Multiple Choice Question An engineer measures the weights (in kilograms) of steel pieces. They would like to test H. : x = 5 against H : > 5. The weights follow a normal distribution with variance 16. Using a sample of size n = 25, the engineer decides to reject He if T > 6. Determine the probability of committing an error of Type I error. A. 0.0500 B. 0.1057 C. 0.8943 D. 0.1000 E. none of the preceding
3. Multiple Choice Question An engineer measures the weights (in kilograms) of steel pieces. They would like to test H: = 5 against H: > 5. The weights follow a normal distribution with variance 16. Using a sample of size n = 25, the engineer decides to reject Hif I > 6. Assuming that the true population mean is 5.2, determine the probability of committing an error of Type II error A. 0.8413 B. 0.05 C. 0.9332 D. 0.8943 E....
20. Multiple Choice Question An engineer measures the weights (in kilograms) of steel pieces. They would like to test Ho : = 5 against HL : H > 5. The weights follow a normal distribution with variance 16. Using a sample of size n = 25, the engineer decides to reject H, if 7 > 6. Assuming that the true population mean is 5.2, determine the probability of committing an error of Type II error. A. 0.8413 B. 0.05 C....
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