In hypothesis testing, a type 2 error occurs when A. The null hypothesis is not rejected when it is true. Say no to plagiarism. Get a tailor-made essay on “Why Violent Video Games Should Not Be Banned”? Get the original essayB. The null hypothesis is rejected when it is true.C. The null hypothesis is not rejected when the alternative hypothesis is true.D. The null hypothesis is rejected when the alternative hypothesis is true. A hypothesis test is performed in which the alternative hypothesis is that more than 10% of a population is left-handed. The p-value for the test is calculated as 0.25. Which statement is correct?A. We can conclude that more than 10% of the population is left-handed.B. We can conclude that more than 25% of the population is left-handed.C. We can conclude that exactly 25% of the population is left-handed.D. We cannot conclude that more than 10% of the population is left-handed. A significance test based on a small sample may not produce a statistically significant result even if the true value differs significantly from the null value. This type of result is called A. the significance level of the test.B. the power of study.C. a type 1.D error. a type 2 error. A result is said to be “statistically significant” whenever A. The null hypothesis is true.B. The alternative hypothesis is true.C. The p-value is less than or equal to the significance level.D. The p-value is above the significance level. Null and alternative hypotheses are statements about: A. population parameters.B. Sample parameters.C. examples of statistics.D. it depends - sometimes on population parameters and sometimes on sample statistics. Problem 38. Acme Corporation manufactures light bulbs. The CEO says the average Acme bulb lasts 300 days. A researcher randomly selects 15 bulbs to test. The bulbs sampled lasted an average of 290 days, with a standard deviation of 50 days. If the CEO's statement were true, what is the probability that 15 randomly selected light bulbs would have an average lifespan of no more than 290 days?(A) 0.100(B) 0.226(C) 0.334(D) 0.443(E) ) 0.775SolutionThe answer is (B). The first thing we need to do is calculate the t statistic, based on the following equation: t = [ x - µ ] / [ s / sqrt( n )]t = ( 290 - 300 ) / [ 50 / sqrt( 15) ]t = -10 / 12.909945 = - 0.7745966 where x is the sample mean, µ is the population mean, s is the sample standard deviation and n is the size of the sample 'sample. Then, using an online calculator (e.g., Stat Trek's Free T Distribution Calculator), a portable graphing calculator, or the t distribution chart, we find the cumulative probability associated with the t statistic. For this practical test, we can use the T distribution calculator; but when taking the actual AP Statistics exam, you may need to use a graphing calculator or distribution table. Since we know the t statistic, we select "T score" from the Random variable drop-down list of the T distribution calculator. Next, we enter the following data: The degrees of freedom are equal to 15 - 1 = 14. The t statistic is equal to - 0.7745966. Keep in mind: this is just a sample. Get a personalized article from our expert writers now. Get a Custom EssayThe calculator displays the cumulative probability: 0.226. Therefore, if the actual lifespan of the bulb was 300 days, there is a 22.6% chance that the average lifespan of 15 randomly selected bulbs would be less than or equal to 290 days..