6/14/25, 9:20 AM Graded Exam 3
Topic 6: Hypothesis Testing
Started on Saturday, June 14, 2025, 10:04 AM
State Finished
Completed on Saturday, June 14, 2025, 10:20 AM
Time taken 16 mins
Grade 108.34 out of 125.00 (86.67%)
Question 1
In a hypothesis test for matched or paired samples, the test statistic t𝑡 is calculated using the
Correct formula:
8.33 points out Xd 𝑋‾ 𝑑
of 8.33 t= Sd
𝑡= 𝑆𝑑
√n
Which option correctly defines the variables in this formula?
Select one:
a.
X d 𝑋¯ 𝑑 is the population mean of the differences, Sd 𝑆𝑑 is the population standard deviation,
and n 𝑛 is the number of populations.
b.
X d 𝑋¯ 𝑑 is the median of the differences, Sd 𝑆𝑑 is the variance of the differences, and n𝑛 is the
number of paired samples.
c.
X d 𝑋¯ 𝑑 is the sample mean of the differences, Sd 𝑆𝑑 is the sample variance, and n𝑛 is the
degrees of freedom.
d.
X d 𝑋¯ 𝑑 is the sample mean of the differences, Sd 𝑆𝑑 is the sample standard deviation of the
differences, and n 𝑛 is the sample size.
Question 2
Which of the following best defines the Student's t-distribution?
Incorrect
0.00 points out Select one:
of 8.33 a. A symmetric, bell-shaped distribution used for large sample sizes when the population
standard deviation is known.
b. A probability distribution used when estimating the population mean from a small sample
size and the population standard deviation is unknown.
c. A distribution that describes the probability of independent events occurring in a fixed
interval.
d. A skewed distribution used to model categorical data.
, 6/14/25, 9:20 AM Graded Exam 3
Question 3
In quality control, the Central Limit Theorem is essential for assessing production processes.
Partially correct Suppose a beverage company fills cans with a mean amount of 16.00 ounces and a standard
5.55 points out deviation of 0.143 ounces. If a sample of n = 34 𝑛 = 34 cans is selected and the sample mean is
of 8.33 16.01 ounces, the standard error of the mean is σx =
0.143
≈ 0.0245 𝜎 = ≈ 0.0245 ounces. The
√ 34
z-score is calculated to determine the probability that the sample mean amount is greater than
16.01 ounces, helping the company decide if the filling machines are operating correctly.
1. What is the standard error of the mean for a sample size n = 34 𝑛 = 34 with a population standard deviation
σ = 0.143 𝜎 = 0.143 ounces?
0.143 ounces
0.0245 ounces
0.048 ounces
0.0042 ounces
2. Compute the z-score for a sample mean x = 16.01 𝑥¯ = 16.01 ounces, given μ = 16.00 𝜇 = 16.00 ounces and the standard
error calculated previously.
16.00−16.01 16 . 00 - 16 . 01
z= 0.143
= −0. 0070 𝑧 = 0 . 143
= - 0 . 0070
16.00−16.01 16 . 00 - 16 . 01
z= 0.0245
= −0. 4082 𝑧 = 0 . 0245
= - 0 . 4082
16.01−16.00 16.01 − 16.00
z= 0.0245
= 0.4082 𝑧 = 0.0245
= 0.4082
16.01−16.00 16 . 01 - 16 . 00
z= = 0. 0070 𝑧 = 0 . 143
= 0 . 0070
0.143
3. Based on the z-score calculated, what is the approximate probability that the sample mean is greater than 16.01 ounces?
Approximately 34.13%
Approximately 65.87%
Approximately 5%
Approximately 95%
Topic 6: Hypothesis Testing
Started on Saturday, June 14, 2025, 10:04 AM
State Finished
Completed on Saturday, June 14, 2025, 10:20 AM
Time taken 16 mins
Grade 108.34 out of 125.00 (86.67%)
Question 1
In a hypothesis test for matched or paired samples, the test statistic t𝑡 is calculated using the
Correct formula:
8.33 points out Xd 𝑋‾ 𝑑
of 8.33 t= Sd
𝑡= 𝑆𝑑
√n
Which option correctly defines the variables in this formula?
Select one:
a.
X d 𝑋¯ 𝑑 is the population mean of the differences, Sd 𝑆𝑑 is the population standard deviation,
and n 𝑛 is the number of populations.
b.
X d 𝑋¯ 𝑑 is the median of the differences, Sd 𝑆𝑑 is the variance of the differences, and n𝑛 is the
number of paired samples.
c.
X d 𝑋¯ 𝑑 is the sample mean of the differences, Sd 𝑆𝑑 is the sample variance, and n𝑛 is the
degrees of freedom.
d.
X d 𝑋¯ 𝑑 is the sample mean of the differences, Sd 𝑆𝑑 is the sample standard deviation of the
differences, and n 𝑛 is the sample size.
Question 2
Which of the following best defines the Student's t-distribution?
Incorrect
0.00 points out Select one:
of 8.33 a. A symmetric, bell-shaped distribution used for large sample sizes when the population
standard deviation is known.
b. A probability distribution used when estimating the population mean from a small sample
size and the population standard deviation is unknown.
c. A distribution that describes the probability of independent events occurring in a fixed
interval.
d. A skewed distribution used to model categorical data.
, 6/14/25, 9:20 AM Graded Exam 3
Question 3
In quality control, the Central Limit Theorem is essential for assessing production processes.
Partially correct Suppose a beverage company fills cans with a mean amount of 16.00 ounces and a standard
5.55 points out deviation of 0.143 ounces. If a sample of n = 34 𝑛 = 34 cans is selected and the sample mean is
of 8.33 16.01 ounces, the standard error of the mean is σx =
0.143
≈ 0.0245 𝜎 = ≈ 0.0245 ounces. The
√ 34
z-score is calculated to determine the probability that the sample mean amount is greater than
16.01 ounces, helping the company decide if the filling machines are operating correctly.
1. What is the standard error of the mean for a sample size n = 34 𝑛 = 34 with a population standard deviation
σ = 0.143 𝜎 = 0.143 ounces?
0.143 ounces
0.0245 ounces
0.048 ounces
0.0042 ounces
2. Compute the z-score for a sample mean x = 16.01 𝑥¯ = 16.01 ounces, given μ = 16.00 𝜇 = 16.00 ounces and the standard
error calculated previously.
16.00−16.01 16 . 00 - 16 . 01
z= 0.143
= −0. 0070 𝑧 = 0 . 143
= - 0 . 0070
16.00−16.01 16 . 00 - 16 . 01
z= 0.0245
= −0. 4082 𝑧 = 0 . 0245
= - 0 . 4082
16.01−16.00 16.01 − 16.00
z= 0.0245
= 0.4082 𝑧 = 0.0245
= 0.4082
16.01−16.00 16 . 01 - 16 . 00
z= = 0. 0070 𝑧 = 0 . 143
= 0 . 0070
0.143
3. Based on the z-score calculated, what is the approximate probability that the sample mean is greater than 16.01 ounces?
Approximately 34.13%
Approximately 65.87%
Approximately 5%
Approximately 95%
