In hypothesis testing, a type 2 error occurs whenA. The null hypothesis is not rejected when the null hypothesis is true. Say no to plagiarism. Get a tailor-made essay on "Why Violent Video Games Shouldn't Be Banned"? Get an original essayB. The null hypothesis is rejected when the null hypothesis 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 where the alternative hypothesis is that more than 10% of the population is left-handed. The p-value for the test is calculated to be 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 substantially from the null value. This type of result is known as 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 greater than the significance level. The null and alternative hypotheses are statements about: A. population parameters.B. sample parameters.C. sample statistics.D. it depends: sometimes population parameters and sometimes sample statistics. Problem 38 Acme Corporation produces light bulbs. The CEO claims that the average Acme bulb lasts 300 days. A researcher randomly selects 15 light bulbs to test. The bulbs sampled last 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 have an average life 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 = - 0.7745966where x is the sample mean, µ is the population mean, s is the standard deviation of the sample and n is the sample size. Then, using an online calculator (for example, Stat Trek's free T-distribution calculator), a portable graphing calculator, or the t-distribution table, we find the cumulative probability associated with the t-statistic. For this practical test we can use the T distribution calculator; but on 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 box of the T-distribution calculator. Then, we enter the following data: The degrees of freedom equals 15 - 1 = 14. The t-statistic equals - 0.7745966. Please note: this is just an example. Get a custom paper from our expert writers now. Get a Custom EssayThe calculator shows the cumulative probability: 0.226. Therefore, if the actual bulb life was 300 days, there is a 22.6% chance that the average bulb life for 15 randomly selected bulbs would be less than or equal to 290 days..