"A movie data base claims that the average length of movies is 117 minutes. A researcher collected a random sample of 160 movies released during 2010–2015. The mean length of those movies is 118.44 minutes and the standard deviation is 8.82. The researcher wonders if the actual mean length of movies released during 2010-2015 is more than the data base value and wants to carry out a hypothesis test. What are the null and alternative hypothesis?"

 In a hypothesis test, the null hypothesis (often denoted as H₀) is a statement of no effect or no difference, and it is the hypothesis that the researcher tries to disprove. The alternative hypothesis (denoted as H₁ or Ha) is the statement that indicates the presence of the effect or difference that the researcher is testing for.

Here, the movie database claims that the average length of movies is 117 minutes. The researcher's sample suggests that the average might be longer for movies released between 2010 and 2015, based on their sample mean of 118.44 minutes.

Therefore, the null and alternative hypotheses for this scenario would be:

Null hypothesis (H₀): μ = 117 The null hypothesis states that the true mean length of the movies released during 2010–2015 is equal to the claimed average of 117 minutes.

Alternative hypothesis (H₁ or Ha): μ > 117 The alternative hypothesis asserts that the actual mean length of movies released during 2010-2015 is greater than 117 minutes.

The researcher can now proceed with the hypothesis test, often using a t-test or z-test (depending on whether the population standard deviation is known or if the sample size is large), to decide if the null hypothesis can be rejected in favor of the alternative hypothesis based on the evidence provided by the sample data.