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Math Help - very last statistics questions

  1. #1
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    very last statistics questions

    The manufacturer’s recommended air pressure for a certain type of tire is 32 psi. A random sample of n=35 such tires from different cars operated by a large rental company yields a sample average pressure and sample standard deviation of 31.4 and 1.2, respectively. Does this data suggest that the average pressure for all such tires on that rental company‘s cars differs from the recommended value?


    To get the p-value my teacher used the Standard normal distribution, but shouldn't we use the student t distributon, because we have sample standard deviation not the population data?

    Thank you.
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    Quote Originally Posted by 0123 View Post
    The manufacturer’s recommended air pressure for a certain type of tire is 32 psi. A random sample of n=35 such tires from different cars operated by a large rental company yields a sample average pressure and sample standard deviation of 31.4 and 1.2, respectively. Does this data suggest that the average pressure for all such tires on that rental company‘s cars differs from the recommended value?


    To get the p-value my teacher used the Standard normal distribution, but shouldn't we use the student t distributon, because we have sample standard deviation not the population data?

    Thank you.
    The t-test is used when population sd isn't known - and when the sample size is 'small'. However, if the sample is sufficiently 'large' the z-test can be used.

    How large is 'large' you might reasonably ask ....

    The rule of thumb I was taught (there is actually a mathematical justification) is n > 50. However, you'll find others who say n > 40, and others again who say n > 30. Your teacher is probably in the n > 30 camp.
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