A consumer product magazine recently ran a story concerning the increasing price

Question

A consumer product magazine recently ran a story concerning the increasing price of VCR's. The story stated that the VCR prices dipped in the early 1990's but now are beginning to skyrocket in price. According to the story, the average price of a VCR in 1992 was $211. Use the statistix to answer the question regarding history. A sample test for VCR price Null hypothesis: MU= 211 Alternative hypothesis: MU> 211 Mean 241.23 STD error 15.62 Mean- Ho 30.23 T 1.935 D.F. 19 P. .0340 Cases included 20 What assumption must be satisfied in order for these results to be valid? A) the sample size of 20 VCR prices must possess an approximate t distribution with 19 degrees of freedom B.) the population of all VCR prices must possess an approximate t distribution with 19 degrees if freedom C). The sampling distribution of the sample mean must possess an approximately normal distribution D). The population of all VCR prices must posees an approximately normal distribution A consumer product magazine recently ran a story concerning the increasing price of VCR's. The story stated that the VCR prices dipped in the early 1990's but now are beginning to skyrocket in price. According to the story, the average price of a VCR in 1992 was $211. Use the statistix to answer the question regarding history. A sample test for VCR price Null hypothesis: MU= 211 Alternative hypothesis: MU> 211 Mean 241.23 STD error 15.62 Mean- Ho 30.23 T 1.935 D.F. 19 P. .0340 Cases included 20 What assumption must be satisfied in order for these results to be valid? A) the sample size of 20 VCR prices must possess an approximate t distribution with 19 degrees of freedom B.) the population of all VCR prices must possess an approximate t distribution with 19 degrees if freedom C). The sampling distribution of the sample mean must possess an approximately normal distribution D). The population of all VCR prices must posees an approximately normal distribution A consumer product magazine recently ran a story concerning the increasing price of VCR's. The story stated that the VCR prices dipped in the early 1990's but now are beginning to skyrocket in price. According to the story, the average price of a VCR in 1992 was $211. Use the statistix to answer the question regarding history. A sample test for VCR price Null hypothesis: MU= 211 Alternative hypothesis: MU> 211 Mean 241.23 STD error 15.62 Mean- Ho 30.23 T 1.935 D.F. 19 P. .0340 Cases included 20 What assumption must be satisfied in order for these results to be valid? A) the sample size of 20 VCR prices must possess an approximate t distribution with 19 degrees of freedom B.) the population of all VCR prices must possess an approximate t distribution with 19 degrees if freedom C). The sampling distribution of the sample mean must possess an approximately normal distribution D). The population of all VCR prices must posees an approximately normal distribution

Explanation / Answer

When conducting a t test, we have the following assumptions:

1) The scale of measurement applied to the data collected follows a continuous or ordinal scale.

2) The second assumption made is that of a simple random sample, that the data is collected from a representative, randomly selected portion of the total population.

3) The third assumption is that the data, when plotted, results in a normal distribution, bell-shaped distribution curve.

4) The sample size is < 30

Hence the answer to your question is OPTION C : The sampling distribution of the sample mean must possess an approximately normal distribution

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