Question

You have a part-time job delivering groceries, and over eight days, you get the following income from tips: $20.80, $21.45, $17.30, $21.05, $19.75, $16.85, $17.25, $20.25.

(a) Compute the sample mean and sample standard deviation for your daily tips.

(b) Suppose you want to test the hypothesis H0 : µ = 19.5 versus Ha : µ 6= 19.5. Find the test statistic and P-value.

(c) Can we reject the null hypothesis at the level α = 0.01?

(d) Compute a two-sided 95% confidence interval for your daily tips

Answer 1

Answers 1 x sample data is given by 20.80 , 21.45, 17.30 , 21.05, 19.75 , 16.85, | 17.25 , 20.25 n 8 Sample mean Ž = EXi = 154. = 19.33 Sample standard deviation is given 9 Tex:? ng² 3 016.765-8X(19.2212 n-1 7 Is = 1.8986 b) consider Horell = 19.5 the testing vis: Haiell $ 18.5 .: Test statistic is given by t = X-4 a toale - s/n t = 19.33- 19.5 1.8986/ve E = -0.2532 from statistical table .: 77,0.01 = 4,03

g. It) € 77,001 We accept the null hypothests at delet d) 95% Confidence internal is given by (x- tn-l s X+ tn-i, a 5 ha 19.33 +603 x. 1.8985 19.23 -4.03 x 1.8986_ 18 [ 16.624 624 22.035) ,035