Question

2. In 2001, 38% of families reported that their family regularly ate dinner together. A researcher at this proportion has decreased. In a recent poll, 35.9% of 1122 families reported that their family regularly ate dinner together. Use a = 0.05 You may use the 1-PropZTest on your graphing calculator. (a) State the null and alternative hypotheses. (b) This time p = 0.359 and n = 1122 are given to you. Find x = np. (You will need to round the result to the nearest whole number.) (c) Give the test statistic (round to 2 decimal places): 2 = (d) Give the P-value (round to 3 decimal places) (e) State your decision. (f) State your conclusion.

Please answer each question and show work.

Answer 1

a) Test hypothesis Ho:p=0.38 H:p<0.38 (claim) Given sample size n=1122 Sample proportion p = 0.359 b) x =n*p = 1122*0.359 = 402.798 c) Test statistic z = 5p(1-P)/n 0.359-0.38 70.38(1-0.38)/1122 =-1.45

P-value =P(z<-1.45)=0.0735 Since p-value >0.05 hence fail to reject the null hypothesis There is insufficient evidence to conclude that the proportion of families regularly ate dinner together is less than 38%