In a test of hypotheses, a researcher used the level of significance α = 0.05. Based on a random sample, she obtained a P-value of 0.052. Which of the following is strictly true for this level of significance and conditions?

In testing hypotheses, if the consequences of rejecting the null hypothesis are very serious, we should

The Survey of Study Habits and Attitudes (SSHA) is a psychological test that measures the motivation, attitudes, and study habits of college students. Scores range from 0 to 200 and follow (approximately) a Normal distribution, with mean of 115 and standard deviation 25. A researcher suspects that incoming freshmen have a mean μ, which is different from 115, because they are often excited yet anxious about entering college. To verify her suspicion, she tests the hypotheses

H0: μ = 115

Ha: μ ≠ 115.

The researcher gives the SSHA to 100 incoming freshmen and observes a mean score of 119. Assume that the scores of all incoming freshmen are approximately Normal with the same standard deviation as the scores of all college students.

If the researcher deems the data to be statistically significant, which of the following is true with respect to a conclusion reached?

Suppose in a test of hypotheses, data are deemed to be significant at level α = 0.08, but not significant at level α = 0.04. Which of the following is true about the P-value, P, associated with this test?

In a statistical test of hypotheses, we say the data are statistically significant at level α if

The Survey of Study Habits and Attitudes (SSHA) is a psychological test that measures the motivation, attitudes, and study habits of college students. Scores range from 0 to 200 and follow (approximately) a Normal distribution, with mean of 115 and standard deviation 25. A researcher suspects that incoming freshmen have a mean μ, which is different from 115, because they are often excited yet anxious about entering college. To verify her suspicion, she tests the hypotheses

H0: μ = 115

Ha: μ ≠ 115.

The researcher gives the SSHA to 100 incoming freshmen and observes a mean score of 119. Assume that the scores of all incoming freshmen are approximately Normal with the same standard deviation as the scores of all college students.

[Hint: firstly determine the test statistic, then use an appropriate table and consider the nature of the alternative hypothesis]

An engineer designs an improved automobile engine for a certain make of automobile. The previous design had an average highway petrol consumption of 10.0 l/km (litres per 100 kilometres) with a standard deviation of 0.5 l/km. The new engine has an average highway petrol consumption of 9.8 l/km, based on a sample of 3600 cars of the model with the new engine. A test of significance for the mean petrol consumption of the new engine is conducted. Based on this sample, the Z-statistic associated with this test of significance is (no units required). Round to no decimal places.

Is the mean age at which Australian children can first read now under four years? If the population of all Australian children has a mean age of μ years until they begin to read and standard deviation σ years, one would test which of the following null and alternative hypotheses to research this?

In formulating hypotheses for a statistical test of significance, the null hypothesis is often

In statistical hypothesis testing, a result from a data set has statistical significance when