1. The sample is representative of the population.

This condition might not be fully satisfied. The student only bought and weighed the first 10 packets on the shelf at their local supermarket. This might not be a truly random sample, and it might not accurately represent all 100g packets of potato chips from the supermarket or the broader population of all 100g packets of potato chips. The packets at the front of the shelf could be different from those at the back (for example, if they were stocked at different times or come from different batches).

Answer: Not Satisfied

2. The sampling distribution of the sample mean is normal.

The Central Limit Theorem (CLT) states that if you have a population with mean μ and standard deviation σ and take sufficiently large random samples from the population with replacement, then the distribution of the sample means will be approximately normally distributed. This will hold true regardless of whether the source population is normal or skewed, provided the sample size is sufficiently large (usually n 30).

In this case, the sample size is 10, which is less than 30. Therefore, according to the CLT, we cannot assume that the sampling distribution of the sample mean is approximately normal. However, if the original population of potato chip packet weights is normally distributed, then the sample mean could still be normally distributed. Without more information, we cannot definitively say whether this condition is satisfied.

Answer: Not Satisfied (without additional information)

Question

1. The sample is representative of the population.

This condition might not be fully satisfied. The student only bought and weighed the first 10 packets on the shelf at their local supermarket. This might not be a truly random sample, and it might not accurately represent all 100g packets of potato chips from the supermarket or the broader population of all 100g packets of potato chips. The packets at the front of the shelf could be different from those at the back (for example, if they were stocked at different times or come from different batches).

Answer: Not Satisfied

2. The sampling distribution of the sample mean is normal.

The Central Limit Theorem (CLT) states that if you have a population with mean μ and standard deviation σ and take sufficiently large random samples from the population with replacement, then the distribution of the sample means will be approximately normally distributed. This will hold true regardless of whether the source population is normal or skewed, provided the sample size is sufficiently large (usually n > 30).

In this case, the sample size is 10, which is less than 30. Therefore, according to the CLT, we cannot assume that the sampling distribution of the sample mean is approximately normal. However, if the original population of potato chip packet weights is normally distributed, then the sample mean could still be normally distributed. Without more information, we cannot definitively say whether this condition is satisfied.

Answer: Not Satisfied (without additional information)

Knowee AI · Accepted Answer

1. The sample is representative of the population.

This condition might not be fully satisfied. The student only bought and weighed the first 10 packets on the shelf at their local supermarket. This might not be a truly random sample, and it might not accurately represent all 100g packets of potato chips from the supermarket or the broader population of all 100g packets of potato chips. The packets at the front of the shelf could be different from those at the back (for example, if they were stocked at different times or come from different batches).

Answer: Not Satisfied

2. The sampling distribution of the sample mean is normal.

The Central Limit Theorem (CLT) states that if you have a population with mean μ and standard deviation σ and take sufficiently large random samples from the population with replacement, then the distribution of the sample means will be approximately normally distributed. This will hold true regardless of whether the source population is normal or skewed, provided the sample size is sufficiently large (usually n > 30).

In this case, the sample size is 10, which is less than 30. Therefore, according to the CLT, we cannot assume that the sampling distribution of the sample mean is approximately normal. However, if the original population of potato chip packet weights is normally distributed, then the sample mean could still be normally distributed. Without more information, we cannot definitively say whether this condition is satisfied.

Answer: Not Satisfied (without additional information)

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