A peony plant with red petals was crossed with another plant having streaky petals. A geneticist states that 75% of the offspring from this cross will have red flowers. To test this claim, 100 seeds from this cross were collected and germinated, and 52 plants had red petals. Use the chirsquare goodnessaofrfit test to determine whether the sample data confirm the geneticist's prediction. (Use c: = 0.01. Use [)1 for the probability of having red flowers and p2 for the probability of having streaky petals.) State the null and alternative hypotheses Find the test statistic. Find the rejection region. State your conclusion. _ Let's organize the data into a table. One category is offspring with red petals and the second category is offspring with streaky petals The geneticist germinated 100 seeds and found 52 of the plants had red petals. Complete the following table Red Petals Streaky Petals Observed Count 52 100 a 52 : \\:| We are asked to determine whet1er the geneticist's claim of 75% of the offspring from the cross of these two peony plants will have red petals is correct. By deduction we can conclude that the streaky petals category will have a rate of 100% 75% : 25% among the offspring. Let's define these two categories with p1 representing the probability of having red petals and p2 representing the probability of having streaky petals. State the null and alternative hypotheses. O HO: p1 : 0.52; Dz : 0.48 Ha: At least one ,0] is different from the specified value. - O HO: At least one p, is different from the specified value. Ha' p1 : 0.52; p2 : 0.48 O HO: p1 : 0.75; oz : 0.25 Ha: At least one ,0] is different from the specified value. O HO: p1 = p2 = 0.5 Ha. At least one p] is different from 0.5. (I) H0: At least one p, is different from the specified value. Ham1 = 0.75; p2 = 0.25 Suppose that a consumer survey summarizes the responses of n = 363 people in a contingency tabie that contains six rows and five coiumns. How many degrees of freedom are associated with the chisquare test statistic? S degrees of freedom A survey of 400 respondents produced these ceii counts in a 2 x 3 contingency table. Columns Rows 1 2 3 Total 1 35 35 94 167 2 67 57 109 233 Total 105 92 203 400 (a) If you wish to test the null hypothesis of "independence"that the probability that a response falls in any one row is independent of the column it fails inand you plan to use a chi-square test, how many degrees of freedom will be associated with the X2 statistic? E degrees of Freedom (b) Find the value of the test statistic. (Round your answer to three decimal piaces.) (c) Find the rejection region for a = 0.01. (Round your answer to three decimal places.) A study was conducted to determine the effect of early child care on infant-mother attachment patterns. In the studyj 88 infants were classied as either \"secure\" or "anxious\" using the Ainsworth strange situation paradigm. In addition, the infants were classified according to the average number of hours per week that they spent in child care. The data are presented in the table Low Moderate High (03 hours) (419 hours) (2054 hours) Secure 22 35 5 Anxious 12 8 6 (a) Do the data provide sufficient evidence to indicate that there is a difference in attachment pattern for the infants depending on the amount of time spent in child care? Test using a : 0.05. State the null and alternative hypotheses. O HO: Attachment pattern and amount of time spent in child care are dependent. Ha: Attachment pattern and amount of time spent in child care are independent. O HO: Attachment pattern and amount of time spent in child care are linearly related. Ha' Attachment pattern and amount of time spent in child care are independent. 0 H0: Attachment pattern and amount of time spent in child care are independent Ha' Attachment pattern and amount of time spent in child care are dependent. O HO: Attachment pattern and amount of time spent in child care are independent Ha' Attachment pattern and amount of time spent in child care are linearly related 0 H0: The number of secure and anxious children are equal H3' The number of secure and anxious children are not equal. Find the test statistic. (Round your answer to three deCimal places.) Xe: Find the rejection region. (Round your answer to three decimal places.)