A psychologist is studying smokers' self-images, which she measures by the self-image (SI) score from a personality inventory. For adults in the U.S., the mean SI score from this inventory is about 140. The psychologist gathers a random sample of 20 SI scores of smokers and finds that their mean is 121 and their standard deviation is 31. Assume that the population of SI scores of smokers is normally distributed with mean u. Based on the sample, can the psychologist conclude that u is different from 140? Use the 0.05 level of significance. Perform a two-tailed test. Then complete the parts below. Carry your intermediate computations to three or more decimal places and round your answers as specified in the table. (If necessary, consult a list of formulas.) (a) State the null hypothesis Ho and the alternative hypothesis H1 O P Ho : X S H, : 0 (b) Determine the type of test statistic to use. (Choose one) =0 050 020 (c) Find the value of the test statistic. (Round to three or more decimal places.) #0 00 X ? (d) Find the p-value. (Round to three or more decimal places.) 0 (e) At the 0.05 level of significance, can the psychologist conclude that the mean SI score among smokers is different from 140? OYes ONo