Assessment

You want to test if a sample of 20 apples has an average weight that is significantly different from the average weight of a local grocery store, you find that the sample average weight is 4.6 ounces. Suppose that the weights of apples at a local grocery store are normally distributed with a population standard deviation of 0.25 ounces. Does this problem require the use of z or t table?

• Only Z table

• Only T table

• Either Z or T table

Answer explanation

This problem requires the use of z table, since it is stated that the problem has a known population standard deviation of 0.25 ounces, a normal population distribution, and a small sample size of 20 apples.

A company claims that their new product increases customer satisfaction from 6.0 to 7.0. To test this, a sample of 12 customers was chosen and their satisfaction level was measured, they found out that the sample mean was 6.8 with a standard deviation of 0.7. Does this problem require the use of z or t table?

• Only Z table

• Only T table

• Either Z or T table

Answer explanation

For this problem, we can use the t table, due to the information that the problem has unknown population standard deviation, and has a small sample size of 12 customers. The population distribution being normal or not doesn't affect this decision.

A manufacturer of light bulbs claims that the average lifespan of their light bulbs is 10,000 hours with a population standard deviation of 500 hours. To test this claim, a sample of 500 light bulbs are randomly selected and examined. It is determined that the sample average lifespan is 10,100 hours

a)   Assuming that the population distribution is normal, does this problem require the use of z or t table?

• Only Z table

• Only T table

• Either Z or T table

Answer explanation

To solve this problem, we are required to use z table. As mentioned in the problem, it has a known population standard deviation of 500 hours, a normal population distribution, and a large sample size of 500 hours.

A manufacturer of light bulbs claims that the average lifespan of their light bulbs is 10,000 hours with a population standard deviation of 500 hours. To test this claim, a sample of 500 light bulbs are randomly selected and examined. It is determined that the sample average lifespan is 10,100 hours

b)  Suppose the population distribution is not normal, does this problem require the use of z or t table?

• Only Z table

• Only T table

• Either Z or T table

Answer explanation

This problem would require the use of either z or t table, due to the indication

of the problem of having a known population standard deviation of 500 hours, but the population distribution is not normal, and the large sample size of 500 hours

A school claims that the average score of their students in a standardized test is 80 with a population standard deviation of 10. To test this claim, a sample of 15 students was randomly selected and their scores were measured. It turned out that the sample mean was 75 and the standard deviation was 6. Assuming that the population distribution is not normal, does this problem require the use of z or t table?

• Only Z table

• Only T table

• Either Z or T table

Answer explanation

Given that it has a known population standard deviation of 10, that the population distribution is not normal, and that the small sample size of 15 students, we can conclude that the problem requires the use of t table

According to a university, the average height of their students is 5 feet and 8 inches. To verify this claim, the heights of 100 students selected at random were measured. The sample mean was found to be 5 feet and 9 inches, does this problem require the use of z or t table?

• Only Z table

• Only T table

• Either Z or T table

Answer explanation

This problem can be solved by using either z or t table. This problem has an unknown population standard deviation, and has a large sample size of 100 students. Similar to number 2, the population distribution being normal or not doesn’t affect this decision.

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