Question

3. For the Price variable, test the hypothesis of µ being different than 11,500 at the 5% level of significance:

(a) (10 pts) State your null and alternative hypotheses.

(b) (10 pts) Find the relevant p-value and write it down.

(c) (10 pts) What do you conclude, based on your findings?

1 2 3 4 5 6 1 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 Price Age (months) Mileage (km) Weight (kg) 15750 30 57086 1110 22250 20 37500 1260 15950 20 33329 1100 15950 19 25948 1100 17450 18 23902 1100 31000 4 4000 1480 22950 7 10000 1270 17900 7 1105 17950 17 33740 1135 16450 20 22588 1110 16450 16 20105 1110 19750 17 11999 1130 18950 16 11000 1105 18245 9 1 1075 19500 8 10077 1110 18950 8 10000 1110 22500 6 3000 1130 21125 2 225 1110 9950 42 105699 1025 11500 44 89757 1045 13950 44 59000 1110 10850 43 54600 1030 13500 35 48052 1105 12950 39 45081 1075 12500 43427 1040 13950 42 42560 1080 12950 44 41499 1103 12750 37 39757 1075 13500 42 38932 1040 11750 40 32532 1040 11950 42 30190 1075 14950 43 25228 1045 10500 41 22780 1035 11450 37 21500 1030 13250 16512 1085 10500 54 115046 1140 10950 54 96100 1080 8950 53 90200 1025 9950 45 87274 1040 10500 50 83567 1075 10950 50 82735 1030 10895 53 79800 1075 36 30 31 32 33 34 35 33 36 37 38 39 40 41 42

Answer 1

(a) The hypothesis being tested is:

H₀: µ = 11500

H_a: µ ≠ 11500

(b) The p-value is 0.0000.

11,500.0000	hypothesized value
10,117.1100	mean Price
3,069.4837	std. dev.
306.9484	std. error
100	n
99	df
-4.505	t
1.82E-05	p-value (two-tailed)

(c) Since the p-value (0.0000) is less than the significance level (0.05), we can reject the null hypothesis.

Therefore, we can conclude that µ ≠ 11500.