Question
Determine whether the z-test or the t-test should be performed, or whether a statistician should be consulted.
A simple random sample of size 23 has mean x=14.3 and the standard deviation is s=2.45. The population is not approximately normal. Can you conclude that the population mean is less than 10?
The population standard deviation [is or isnt] known.
The sample size n [is or isnt] greater than 30.
The population [is or isnt] approximately normal.
The correct decision is to [perform the z-test? perform the t-test? or talk to a statistician?].
A simple random sample of size 23 has mean x=14.3 and the standard deviation is s=2.45. The population is not approximately normal. Can you conclude that the population mean is less than 10?
The population standard deviation [is or isnt] known.
The sample size n [is or isnt] greater than 30.
The population [is or isnt] approximately normal.
The correct decision is to [perform the z-test? perform the t-test? or talk to a statistician?].
Answers
Answer
A simple random sample of size 13 has mean x=9.4 and standard deviation s=1.9. The population is approximately normally distributed. Can you conclude that the population mean differs from 11?
The population standard deviation [is or isnt?] known.
The sample size n [is or isnt] greater than 30.
The population [is or isnt?] approximately normal.
The correct decision is to [perform the z-test? perform the t-test? or talk to a statistician?].
The population standard deviation [is or isnt?] known.
The sample size n [is or isnt] greater than 30.
The population [is or isnt?] approximately normal.
The correct decision is to [perform the z-test? perform the t-test? or talk to a statistician?].
Answer
A simple random sample of size 28 has mean x=41.8. The population standard deviation is σ=3.8. The population is normally distributed. Can you conclude that the population mean is greater than 40?
The population standard deviation [is or isnt] known.
The sample size n [is or isnt] greater than 30.
The population [is or isnt] approximately normal.
The correct decision is to [perform the z-test? perform the t-test? or talk to a statistician?].
The population standard deviation [is or isnt] known.
The sample size n [is or isnt] greater than 30.
The population [is or isnt] approximately normal.
The correct decision is to [perform the z-test? perform the t-test? or talk to a statistician?].
Answered by
GPT-4o mini
To determine which statistical test to use, let's evaluate the provided information step by step:
1. **Population Standard Deviation**: You mentioned that the population standard deviation is **not known**. This is important because the t-test is generally used when the population standard deviation is unknown.
2. **Sample Size**: The sample size (\( n = 23 \)) is **not greater than 30**. Typically, when the sample size is small (less than 30), the t-test is preferred, especially if the population is not approximately normal.
3. **Normality of the Population**: The population is **not approximately normal**. Since the sample size is small and the population distribution is not normal, this adds further emphasis on using the t-test.
Given these points, the correct decision is to:
- The population standard deviation is **not known**.
- The sample size \( n = 23 \) is **not greater than 30**.
- The population **is not approximately normal**.
Therefore, the correct decision is to **talk to a statistician** since the conditions for performing a t-test are not satisfied due to the non-normality of the population and the small sample size. Using a t-test could lead to unreliable results in this scenario.
1. **Population Standard Deviation**: You mentioned that the population standard deviation is **not known**. This is important because the t-test is generally used when the population standard deviation is unknown.
2. **Sample Size**: The sample size (\( n = 23 \)) is **not greater than 30**. Typically, when the sample size is small (less than 30), the t-test is preferred, especially if the population is not approximately normal.
3. **Normality of the Population**: The population is **not approximately normal**. Since the sample size is small and the population distribution is not normal, this adds further emphasis on using the t-test.
Given these points, the correct decision is to:
- The population standard deviation is **not known**.
- The sample size \( n = 23 \) is **not greater than 30**.
- The population **is not approximately normal**.
Therefore, the correct decision is to **talk to a statistician** since the conditions for performing a t-test are not satisfied due to the non-normality of the population and the small sample size. Using a t-test could lead to unreliable results in this scenario.
Answered by
GPT-4o mini
To determine which statistical test to use, let's evaluate the provided information:
1. **Population Standard Deviation**: It is indicated that the population standard deviation is **not known**. Therefore, since we don't have this information, we typically use the t-test when the population standard deviation is unknown.
2. **Sample Size**: The sample size \( n = 13 \) is **not greater than 30**. When the sample size is small, the t-test is generally preferred, especially when the population is normally distributed.
3. **Normality of the Population**: The population is stated to be **approximately normal**. This is crucial because the t-test is appropriate to use when the sample size is small and the population is approximately normally distributed.
Given these points, the correct decision is:
- The population standard deviation is **not known**.
- The sample size \( n = 13 \) is **not greater than 30**.
- The population **is approximately normal**.
Therefore, the correct decision is to **perform the t-test**.
1. **Population Standard Deviation**: It is indicated that the population standard deviation is **not known**. Therefore, since we don't have this information, we typically use the t-test when the population standard deviation is unknown.
2. **Sample Size**: The sample size \( n = 13 \) is **not greater than 30**. When the sample size is small, the t-test is generally preferred, especially when the population is normally distributed.
3. **Normality of the Population**: The population is stated to be **approximately normal**. This is crucial because the t-test is appropriate to use when the sample size is small and the population is approximately normally distributed.
Given these points, the correct decision is:
- The population standard deviation is **not known**.
- The sample size \( n = 13 \) is **not greater than 30**.
- The population **is approximately normal**.
Therefore, the correct decision is to **perform the t-test**.
Answered by
GPT-4o mini
To determine which statistical test to use, let's evaluate the provided information:
1. **Population Standard Deviation**: It is indicated that the population standard deviation is **known** (\( \sigma = 3.8 \)). This allows for the use of the z-test.
2. **Sample Size**: The sample size \( n = 28 \) is **not greater than 30**. However, since the population standard deviation is known, we can still proceed with the z-test as long as the population is normally distributed.
3. **Normality of the Population**: The population is stated to be **normally distributed**. This is important because it supports the use of the z-test, particularly when the population standard deviation is known.
Based on this information, we can conclude:
- The population standard deviation is **known**.
- The sample size \( n = 28 \) is **not greater than 30**.
- The population **is normally distributed**.
Given these points, the correct decision is to **perform the z-test**.
1. **Population Standard Deviation**: It is indicated that the population standard deviation is **known** (\( \sigma = 3.8 \)). This allows for the use of the z-test.
2. **Sample Size**: The sample size \( n = 28 \) is **not greater than 30**. However, since the population standard deviation is known, we can still proceed with the z-test as long as the population is normally distributed.
3. **Normality of the Population**: The population is stated to be **normally distributed**. This is important because it supports the use of the z-test, particularly when the population standard deviation is known.
Based on this information, we can conclude:
- The population standard deviation is **known**.
- The sample size \( n = 28 \) is **not greater than 30**.
- The population **is normally distributed**.
Given these points, the correct decision is to **perform the z-test**.
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