Please help by explaining the concepts underlying how the following problems are solved
Peaaphids , Acyrthosiphon pisum , are small , wingless , sapsucking insects that live on plants . They evade predators ( such as ladybugs ) by dropping off . A study examined the mechanism of aphid drops . Researchers placed aphids on a leaf positioned at four different heights ( in centimeters , cm ) above a surface covered with petroleum jelly . When a ladybug was introduced , the aphids dropped , and the petroleum jelly helped capture their landing posture ( upright or not ) . Each aphid performed this experiment only once , at a randomly selected dropping height . The findings are given in the table . \\Dropping Height Landing Posture* 3 cm | 5 cm | 10 cm* 20 cm* Upright 20 23 27 29 Not upright 10 Sample size 30 30 30 30 To access the complete data set , click the link for your preferred software format Excel Minitab IMP SPSS II R Mac- IXT PC-IXT CSV CrunchIt ! The null hypothesis " no relationship, " says that in the population of aphids , the proportions that land upright are the same* when the dropping height is 3 , 5, 10 , and 20 cm . The two - way table contains expected cell counts if this hypothesis is true . Landing Posture 3 cm| 5 cm| 10 cm| 20 cm| Total Upright 24.75| 24.75 | 24.75 \\24.75 99 Not upright 5.25 5.25 5. 25 5.25 5.25 Total 30 30 30 30 30 ( a ) Use the study findings to obtain the value of the chi- square statistic . ( Enter your answer rounded to two decimal places . ) x - = 7.81 ( b) Use software to obtain the related P- value . ( Enter your answer rounded to four decimal places . ) 1 = 0. 0501 ( C ) Is the P- value significant at the 0. 05 level ? Choose the correct interpretation . The P- value is statistically significant at the 0. 05 level . The study provides evidence of no relationship between dropping height and landing posture in the aphid population ( the proportion of upright landing in this population is the same for all four dropping heights ) .* The P- value is statistically significant at the 0. 05 level . The study provides evidence of a relationship between dropping height and landing posture in the aphid population ( the proportion of upright landing in this population is not the same for all four dropping heights ) . The P- value is not statistically significant at the 0. 05 level . The study fails to provide evidence of a relationship between dropping height and landing posture in the aphid population . The P- value is not statistically significant at the 0. 0'S level . The study fails to provide evidence of no relationship* between dropping height and landing posture in the aphid population . O We cannot conclude from the P- value because the conditions for the chi- square test are not met
