Quiz #4

• A random sample of 250 students at a university finds that these students take a mean of 15.4 credit hours per quarter with a standard deviation of 1.7 credit hours. The 90% confidence interval for the mean is 15.4 +/- 0.177. The interval can be interpreted as:

  We are 90% confident that the average number of credit hours per quarter of students at the university falls in the interval of 15.223 to 15.577 hours.
• A 90% confidence interval for the mean percentage of airline reservations being canceled on the day of the flight is (1.5%, 4.2%). What is the point estimator of the mean percentage of reservations that are canceled on the day of the flight?

  2.85%
• A retire statistician was interested in determining the average cost of a $200,000.00 term life insurance policy for a 60 year old male non-smoker. He randomly sampled 65 subjects (60 year old non-smokers) and constructed the following 95% confidence interval for the mean cost of the term life insurance: ($850, $1050). What value of alpha was used to create this confidence interval?

  0.05
• Find z_α/2 for the given value of α = 0.01.

  2.575
• The director of a hospital wishes to estimate the mean number of people who are admitted to the emergency room during a 24 hour period. The director randomly selects 49 different 24 hour periods and determines the number of admissions for each. For this sample, x̅ = 15.3, and s^2 = 25. Estimate the mean number of admissions per 24 hour period within a 95% confidence interval.

  15.3 +/- 1.4
• Conditions required for a valid small sample confidence interval for μ:

  • A random sample is selected from the target population
  • The population has a relative frequency distribution that is approx. normal
• Conditions required for a valid large sample confidence interval for p:

  • A random sample is selected from the target population
  • The sample size (n) is large (both np and nq are >/= 15)
• Sampling error (SE): the half width of a confidence interval.
• Statistical hypothesis: a statement about the numerical value of a population parameter.
• Null hypothesis (H_0): the hypothesis that will be assumed to be true unless the data provide convincing evidence that is false.
• Alternative hypothesis (H_a): the hypothesis that will be accepted only if the data provide convincing evidence of its truth.
• State the null and alternative hypotheses of the following: Whether the mean increase in blood pressure of patients who take a new drug is less than 3 points?

  Null (H_0): μ = 3

  Alternative (H_a): μ < 3
• State the null and alternative hypotheses of the following: Whether the manufacturer of a type of printer can advertise that the mean life of its printheads is at least 1 million characters?

  Null (H_0): μ = 1

  Alternative (H_a): μ < 1
• State the null and alternative hypotheses of the following: Whether the majority of registered voters approve of the president's performance?

  Null (H_0): p = 0.5

  Alternative (H_a): p = 0.5
• State the null and alternative hypotheses of the following: Whether the mean pH level in the water of a water-treatment plant differs from 8.5?

  Null (H_0): μ = 8.5

  Alternative (H_a): μ doesn't = 8.5
• Test statistic: a sample statistic, computed from information provided in the sample, that the researcher uses to decide between the null and alternative hypotheses.
• Rejection region: the set of possible values of the test statistic for which the researcher will reject H_0 in favor of H_a.
• Type 1 error: error occurring if the researcher rejects the null hypothesis in favor of the alternative hypothesis when H_0 is true.
• Type 2 error: error occurring if the researcher accepts the null hypothesis when H_0 is false.
• One tailed test of hypothesis: the alternative hypothesis is directional and includes the symbol "<" or ">".
• Two tailed test of hypothesis: the alternative hypothesis does not specify departure from H_0 in a particular direction and is written with the "does not equal" symbol.
• The owner of a Get-A-Away Travel has recently surveyed a random sample of 444 customers to determine whether the mean age of the agency's customers is over 33. The appropriate hypotheses are H_0: μ = 33, H_a: μ > 33.


  If he concludes the mean age is over 33 when it is not, he makes a type 1 error. If he concludes the mean age is not over 33 when it is, he makes a type 2 error.
• A significance level for a hypothesis test is given as α = 0.1. Interpret this value.

  The probability of making a type 1 error is 0.01.