Question

Question 1 You are testing the claim that the proportion of men who own cats is smaller than the proportion of women who own cats, You sample 50 men, and 45% own cats. You sample 130 women, and 85% own cats. Find P (p-bar), as a decimal, rounded to two decimal places. Submit Question Question 2 You are testing the claim that the proportion of men who own cats is significantly different than the proportion of women who own cats. You sample 100 men, and 80% own cats. You sample 80 women, and 30% own cats. Find the test statistic, rounded to two decimal places. Submit Question Question 3 You are testing the claim that the mean GPA of night students is less than the mean GPA of day students. You sample 20 night students, and the sample mean GPA is 2.53 with a standard deviation of 0.68 You sample 25 day students, and the sample mean GPA is 2.09 with a standard deviation of 0.3 Calculate the test statistic, rounded to 3 decimal places Submit Question

Answer 1

Question 1

Required p bars and test statistic

& I Given: 50 to meu, In a sample 45% own cats 0.45 pun & sample proportion for men oma S.E (@m) St. error Foy om (In Pren) 50 0.45 +0.55 = 0.0704 women , Given 130 In a sample of 05% own cats 0.85 women sample Pw proportion for Bw (1-P) 0.05 a 0.15 0.0 313 S.E ( fr ) - Ew (t-ful 130 is To test pm <bw ( proportion of samaller than proportion of women. to pm - pwco Imn pw) -(pm- pw) Test. stélistic T ~ N(0,1) S.E (@ms-fros test le. is

Variance of (pm Pw) - Var (brus 2 + Valse) va (pin) = (0.0704) ² - 0.00495 van (w) = (0.0313) ? 0.000 98/ Va (pm - pw ) = 0.00495 + 0.000981 Oro05931 0.077 S.E (8m - Pw la 10.0005431 SO Test statistic, Bo under claim pm-pwco is 0852 T= (0.45 (taking V 0.077 pm-pw zo -5.1948 LI T T= -5.19

Question 2

Given: In a sample of 100 men, 80% own cats im -0.00 S.E (pen) = 0.80 x 0.20 100 Jo.0016 0.04 Given. in a sample of O wounen 30% own cet 0.30 pw S.E (fw ) = 0:30 0.20 10.00 2625 0.051 (pm) is significantly To test the claim. proportion of different son proportion of women (pu) pm & pw or pm -pw=0 Test statistic T= (pm - pw) - (pmaßw) ~ N(0,1) SE (ne - Foo) Now, von (fm -pw ) - 0.0016 +0.002625 0.00 4225 0.065 Jo.004225 S.E (sm – Fw) under claim: purpw Test statistic 0.80 - 0.30 7.6923 Т. 0.065 7.69 v To

Question 3

Given: In a sample of 20 night students, sample mean à, = 2.53, st der ; 5,= 0.68 0.68 -0.1521 120 st. de of √20 25 students Given: In a sample of day sample noan łz 2.09 st. der 0.3 6ña 11 0.06 st. dew 22 0.3 5 gą claim mean To test test the c) GPA of night stual mean .GPA of day students (X) students is less than rie x <X X, - co Test statistic is 2, - ) - ( x,-1,) T ~ NCOI) St. deo ( *, -27)

Var (x - 5): Va(, ) + Va (5) (0.06)? 2 + (0.1521) O 026 73 0.1635 st. du (na) - J0:02673 X, - Y, CO Test statistic unden claim (2.53 - 2.09 ( loking To = X, -' FEE o ) 01635 To = 2.6911 To = 2.69