Question

A producer of educational videos for toddlers is conducting a test to see if watching his videos increases a toddler's vocabulary. The test consisted of 100 toddlers watching the videos 5 hours a week for 6 weeks. At the end of the test, the mean number of vocabulary words among the 100 toddlers was 258. From prior measurements the producer knows the vocabulary for the corresponding general population of toddlers is normally distributed with a mean of 250 words with a standard deviation of 50 words. The producer must be at least 95% certain of the test result to claim an increase.
At what level of significance would the null hypothesis be rejected? Express your answer at a decimal (not a percent) rounded to three places.

Answer 1

At what level of significance would the null hypothesis be rejected?

At 0.5% or lower level of significance we can reject H0 : mu = 258

Level of significance = 0.5% = 0.005