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In: Statistics and Probability

Suppose the mean starting salary for nurses is $67,276 nationally. The standard deviation is approximately $10,410....

Suppose the mean starting salary for nurses is $67,276 nationally. The standard deviation is approximately $10,410. The starting salary is not normally distributed but it is mound shaped. A sample of 47 starting salaries for nurses is taken.

State the random variable.

  • The mean starting salary of a nurse.
  • The standard deviation of starting salaries of nurses.
  • Starting salary for a nurse.

What is the mean of the sample mean?
μx̄ =

What is the standard deviation of the sample mean? Round to two decimal places.
σx̄ =

What is the shape of the sampling distribution of the sample mean? Why?

  • You can't say anything about the sampling distribution of the sample mean, since the population of the random variable is not normally distributed and the sample size is greater than 30.
  • You can say the sampling distribution of the sample mean is normally distributed since the sample size is greater than 30.
  • You can say the sampling distribution of the sample mean is not normally distributed since the sample size is greater than 30.

Find the probability that the sample mean is more than $75,000. Round to four decimal places.
P(x̄ > 75000) =

Find the probability that the sample mean is less than $57,000. Round to four decimal places.
P(x̄ < 57000)=

If you did find a sample mean of more than $75,000 would you find that unusual? What could you conclude?

  • It is not unusual to find a sample mean more than $75,000, since the probability is less than 5%. If you find a sample mean more than $75,000, then it may indicate that the population mean has not changed.
  • It is unusual to find a sample mean more than $75,000, since the probability is at least 5%. If you find a sample mean more than $75,000, then it may indicate that the population mean has changed.
  • It is not unusual to find a sample mean more than $75,000, since the probability is at least 5%. If you find a sample mean more than $75,000, then it may indicate that the population mean has not changed.
  • It is unusual to find a sample mean more than $75,000, since the probability is less than 5%. If you find a sample mean more than $75,000, then it may indicate that the population mean has changed.

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orchestra answered 1 year ago
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