Stats

With 98​% ​confidence, based on these​ data, the speed of light is between the lower and upper bounds of the confidence interval.

In​ words, what does the 98% confidence interval​ mean?

If further research is​ conducted, this time using a sample of 500 ​adults, how is the 98​% confidence interval likely to​ change? Explain. Choose the correct answer below.

The confidence interval would likely be narrower because a larger sample would cause the standard error to be smaller.

What type of error is made when a false null hypothesis is not​ rejected?

Type II

The 98​% confidence interval has a greater chance of containing the true mean body temperature of adults than the 90​% confidence​ interval, but the 98​% confidence interval is less precise ​(wider​) than the 90% confidence interval.

What are the advantages and disadvantages of the 98​% confidence​ interval?

Suppose I want to test whether​ students' textbook costs for this semester are higher on average than the average cost of​ $450 in 2000. What would be an appropriate alternative​ hypothesis?

u(special) > 450

The analyst made a Type II error. The actual value was 55.3​ points, which is greater than 52.5.

A human resource analyst wants to know if the applicants this year​ score, on​ average, higher on their placement exam than the 52.5 points the candidates averaged last year. She samples 50 recent tests and finds the average to be 54.1 points. She fails to reject the null hypothesis that the mean is 52.5 points. At the end of the​ year, they find that the candidates this year had a mean of 55.3 points. Choose the correct answer- ______________

The company made a Type II error. The null hypothesis was not​ rejected, but it was false. The true relief rate was greater than 0.25.

A pharmaceutical company tests whether a drug lifts the headache relief rate from the​ 25% achieved by the placebo. They fail to reject the null hypothesis because the​ P-value is 0.465. Further testing shows that the drug actually relieves headaches in​ 38% of people. Choose the correct answer- ___________.

The student did not make an error. The actual value is​ 0.50, which was not rejected.

A student tests 100 students to determine whether other students on her campus prefer soda brand A or soda brand B and finds no evidence that preference for brand A is not 0.5.​ Later, a marketing company tests all students on campus and finds no difference. Choose the correct answer- ____________.

What is the name for the threshold​ p-value that determines when the null hypothesis is​ rejected?

Alpha level

If the​ p-value is smaller than the level of​ significance, what conclusion should we​ reach?

Reject the null hypothesis.

Describe how the​ shape, center, and spread of t​-models change as the number of degrees of freedom increases.

Shape becomes closer to​ Normal, center does not​ change, spread becomes narrower.

A high​ P-value shows that the null hypothesis is true.

This statement is false because a high​ P-value shows that the data is consistent with the null​ hypothesis, but can never prove that the null hypothesis is true.

A very low​ P-value proves that the null hypothesis is false.

This statement is false because a very low​ P-value only shows strong evidence that the null hypothesis is false.

Using an alpha level of​ 0.05, a​ P-value of 0.08 means the null hypothesis is true.

This statement is false because a​ P-value greater than the alpha level only indicates that there is not enough evidence to reject the null hypothesis.

With an alpha level of​ 0.01, a​ P-value of 0.10 results in rejecting the null hypothesis.

This statement is false because only a​ P-value less than the alpha level results in rejecting the null hypothesis.

The alpha level depends on the sample size.

This statement is false because the alpha level is set independently and does not depend on the sample size.

A​ P-value below 0.05 is always considered sufficient evidence to reject a null hypothesis.

This statement is false because the null hypothesis is rejected whenever the​ P-value is below the value of alphaα​, which may not necessarily be 0.05.

Using an alpha level of​ 0.05, a​ P-value of 0.04 results in rejecting the null hypothesis.

This statement is true.

a low​ P-value that provides evidence that the null hypothesis is false.

a low​ P-value that provides evidence that the null hypothesis is false.