Exam 11: Introduction to Hypothesis Testing

A sample is used to obtain a 95% confidence interval for the mean of a population.The confidence interval goes from 78.21 to 87.64.If the same sample had been used to test the null hypothesis that the mean of the population differs from 90,the null hypothesis could be rejected at a level of significance of 0.05.

For a given level of significance,if the sample size is increased,the probability of committing a Type II error will increase.

A sample is used to obtain a 95% confidence interval for the mean of a population.The confidence interval goes from 10.89 to 13.21.If the same sample had been used to test H₀: μ = 12 vs.H₁: μ ≠ 12,H₀ could not be rejected at the 0.05 level.

If a test of hypothesis has a Type I error probability of .05,this means that:

You cannot commit a(n)____________________ error when the null hypothesis is false.

Rechargeable Batteries A researcher wants to study the average lifetime of a certain brand of rechargeable batteries (in hours).In testing the hypotheses,H₀: μ = 950 hours vs.H₁: μ ≠ 950 hours,a random sample of 25 rechargeable batteries is drawn from a normal population whose standard deviation is 200 hours. ​ ​ -{Rechargeable Batteries Narrative} Interpret the meaning of the power of the test.

For a given level of significance,if the sample size is increased,the power of the test will increase.

Suppose we wish to test H₀: μ = 45 vs.H₁: μ > 45.What will result if we conclude that the mean is greater than 45 when the actual mean is 50?

The owner of a local nightclub has recently surveyed a random sample of n = 300 customers of the club.She would now like to determine whether or not the mean age of her customers is over 35.If so,she plans to alter the entertainment to appeal to an older crowd.If not,no entertainment changes will be made.Suppose she found that the sample mean was 35.5 years and the population standard deviation was 5 years.What is the p-value associated with the test statistic?

If a null hypothesis is rejected at the 0.05 level of significance,it must be rejected at the 0.025 level.

The rejection region for testing H₀: μ = 100 vs.H₁: μ ≠ 100,at the 0.05 level of significance is:

A Type II error is defined as:

If a researcher fails to reject a true null hypothesis,he has made a(n)____________________ decision.

The owner of a local Karaoke Bar has recently surveyed a random sample of n = 300 customers of the bar.She would now like to determine whether or not the mean age of her customers is over 35.If so,she plans to alter the entertainment to appeal to an older crowd.If not,no entertainment changes will be made.If she wants to be 99% confident in her decision,what rejection region she use if the population standard deviation σ is known?

Rechargeable Batteries A researcher wants to study the average lifetime of a certain brand of rechargeable batteries (in hours).In testing the hypotheses,H₀: μ = 950 hours vs.H₁: μ ≠ 950 hours,a random sample of 25 rechargeable batteries is drawn from a normal population whose standard deviation is 200 hours. ​ ​ -{Rechargeable Batteries Narrative} Review the results of the previous questions.What is the effect of increasing the sample size on the value of β?

It is possible to directly compare the results of a confidence interval estimate to the results obtained by testing a null hypothesis if:

If we do not reject the null hypothesis,we conclude that there is enough statistical evidence to infer that the null hypothesis is true.

A one-tail p-value is two times the size of a two-tail test.

A(n)____________________ characteristic curve plots the probability of a Type II error for various alternative values of ____________________.

A Type I error occurs when we: