Question

A scientist wants to determine whether or not the height of cacti, in foet, in Africa is significantly higher than the height of Mexican acti. He selects random samples from both regions and following data Africa: Mean - 12.1 Sample size - 201 Mean - 11.2 Sample size - 238 (a) Which of the following would be the correct hypothesis test procedure to determine if the height of cacti, in feet, in Africa is significantly higher than the height of Mexican cacti? Two-sample test for proportions Paired t-test Two-sample t-test (b) What is the value of the sample statistic to test those hypotheses? X (2 decimal places) (c) If the T test statistic is 2.169, and df - 202, find the p-value. 0.030 X (3 decimal places) (d) Select the correct conclusion at pha 0.05 The null hypothesis is rejected. There is sufficient evidence that African cacti arealer on average The null hypothesis is not rejected. There is insufficient evidence that African cacti are taler on average The null hypothesis is rejected. There is insufficient evidence that African cacti are taler on average The hypothesis is not rejected. There is sufficient evidence that African cacti are taller on average

Answer 1

hare To test whether height of cacti in Africa is significante higher than height of mexican cacti. Given: Africa Medico Mean = 12.1 Mean = 11.2 Sample size = 201 sample.Size = 238 correct (a) The test to test for means is two - sample t-test for population means. other two options are wrong as Two-sample test for proportions is to test for proportions (not means) and paired to test is used when samples are not an dependent. coption-3) (b) The sample statistic is 7-8 = 12.1 - 11, 2 = 0.9 , when ã and ģý mean height of Africa and Medico respectively. cati from

69 and df = 202, - Giren the t-test statistic as 2.169 and de the p-value is calculated as 0.015625 (od That is p-value is 0.016 Ccalculated for one- tailed test) as The hypotheses are Ho: M, = 42 Hii M,> M2 (c) At =0.05, the null hypothesis is rejected. There is sufficient evédence that African cacti are taller on average.

Because, P value <0.05. Coption ti (e) The type of error, in context, we might have made is Ture I error, which means the scientist concluded there nificant difference between average height of cach ao Mexico, when in reality there is no difference Coption 4). calue for two-tailed test with t-statistre 2. 169 and df = 202 as 0.0312. That is p-value (two-tailed) Co.05. Hence we reject Ho.