Question

Consider the claim that the average price of a used Toyota Camry in the USA at the time the data was collected was equal to$13,500. Use the variable “Price” to test this claim. (Use the 10% level of significance). Data of price. 7020 17115 17170 17235 17350 17365 17385 17435 17485 17565 17620 17735 17765 17935 17935 17985 18000 18035 18235 18985 17965 7850 7960 8510 8930 9560 9620 9640 9995 10290 10370 10390 10520 11440 6990 7240 8000 8040 8300 8520 8620 9010 9090 9600 10400 10500 11040 11170 12650 13515 14735 12630 13450 13610 13840 14320 15000 15200 15335 16060 16160 16420 16650 16820 16885 16920 17250 17550 17665 14250 14375 14700 15250 17780 18000 19300 19490 10600 10650 10790 11690 12070 12730 12760 12900 13090 13170 13380 13430 13470 13550 13560 13865 14270 14640 14840 14970 15445 17485 18320 15185 16500 17550 11950 12550 12780 12980 13080 13085 13130 13200 13230 13250 13280 13450 13600 13700 13900 13935 13980 14000 14080 14115 14135 14300 11750 16150 16650 17585 17850 17900 17980 18200 18250 18335 18550 18650 18865 18880 24700 23050 6200 7700 8280 9150 9775 10140 10200 13520 8150 8300 9490 9700 10095 10410 10510 10550 10580 10765 12370 14525 9310 11050 14400 15550 15560 15850 15935 16035 16085 16400 16550 16785 18440 18990 18390 12151 12265 12440 12510 12635 12760 12890 13275 13490 13680 13730 13870 14650 15405 16150 16860 18100 12280 12550 12950 13050 13130 13250 13300 13350 13385 13450 13630 13700 13880 13985 14085 14085 14100 14780 14880 14935 15030 15130 15350 15780 21100 15200 15250 15650 15980 16100 16230 16400 16980 17050 17300 19615 15650 8590 10995 11620 12090 9590 10870 11100 11105 11950 13250 15080 15700 16680 17100 18310 15250 10910 14100 14495 14635 16950 12030 12465 12850 12950 13035 13380 13700 14030 14065 14500 14685 14800 17800 7195 7250 7330 7520 7850 8080 8430 9160 9215 10260 11200 8540 8775 8850 9310 9760 11035 11240 12180 14680 10150 10900 11050 11600 11985 12370 12510 12695 12785 12920 13250 13360 13500 13785 13850 13905 13950 14060 14180 14200 14710 14745 14940 15065 15150 15450 15530 15750 15850 16030 16035 16825 18405 11815 12240 12645 13000 13435 13680 13730 13820 13850 14370 14410 14955 15285 15685 16955 12680 13000 13100 13250 13415 13430 14185 16550 15730 16350 16535 16935 17700 17980 19085 24830 6520 6670 6910 7370 8190 8890 9035 9210 9320 11250 11940 8585 8760 8900 8960 9630 9650 9725 10205 10520 10790 11610 12170 13030 12210 12650 13520 13830 13885 14050 14120 14350 14355 15650 16040 16350 16995 17600 18170 11561 12210 12740 12860 13410 13420 13470 13510 13590 13595 13610 13705 15890 12880 13450 14350 16550 16750 17300 17815 4840 6600 7400 7475 7660 8340 8670 8950 10040 10370 7400 8360 8435 10755 10930 9395 13900 11000 11970 11990 12120 12560 12810 13000 13030 13100 7660 8600 8810 8930 9020 9020 9715 9830 10030 10440 7740 8090 9580 10310 10380 11810 10220 10900 11255 10130 12430 12950 13375 13840 14080 14185 14235 14320 14340 15135 15785 15995 16000 16450 16615 16870 17510 17640 18335 18470 19380 12635 15260 12200 12730 13050 15450 15795 16095 16900 15780 15840 11750 12350 12880 13850 14000 15165 19265 5130 7610 8750 9510 9750 9950 10210 11620 8360 8850 9280 10180 12825 12110 15415 14635 16985 17390 16290 12120 12765 12880 13010 13425 14395 15775 16585 12180 13300 13930 15400 17080 15320 8960 7655 8760 9510 9750 10125 11835 12160 12500 12920 13300 13305 13385 13400 13450 13850 13985 14300 14350 14390 14500 14550 14935 15050 15100 15400 15400 15535 15660 15735 16235 17140 17600 17670 17835 17850 18580 19310 14285 15300 15550 11600 12740 12780 12820 13230 14040 14350 14860 15700 16600 21085 12450 12450 12800 12800 12800 12900 12980 13015 13036 13180 13216 13250 13250 14000 19300 19630 15500 16450 16480 18450 18885 26730 5760

Answer 1

The proposed hypothesis in this case is as follows

H0 : = 13500

vs

H1 :   13500

We will use R studio to solve the above problem . Attached is the R code

# Input the values as vector
x <-c(7020, 17115, 17170, 17235, 17350, 17365, 17385, 17435, 17485,
17565, 17620,17735, 17765, 17935, 17935, 17985, 18000 ,18035,
18235, 18985, 17965, 7850, 7960, 8510, 8930, 9560,9620, 9640,9995, 10290, 10370, 10390, 10520, 11440, 6990, 7240, 8000, 8040,
8300, 8520, 8620, 9010, 9090, 9600, 10400, 10500, 11040, 11170,
12650, 13515, 14735, 12630, 13450, 13610, 13840, 14320, 15000,
15200, 15335, 16060, 16160, 16420, 16650, 16820, 16885, 16920,
17250, 17550, 17665, 14250, 14375, 14700, 15250, 17780, 18000,
19300, 19490, 10600, 10650, 10790, 11690, 12070, 12730, 12760,
12900, 13090, 13170, 13380, 13430, 13470, 13550, 13560, 13865,
14270, 14640, 14840, 14970, 15445, 17485, 18320, 15185, 16500,
17550, 11950, 12550, 12780, 12980, 13080, 13085, 13130, 13200,
13230, 13250, 13280, 13450, 13600, 13700, 13900, 13935, 13980,
14000, 14080, 14115, 14135, 14300, 11750, 16150, 16650, 17585,
17850, 17900, 17980, 18200, 18250, 18335, 18550, 18650, 18865,
18880, 24700, 23050, 6200, 7700, 8280, 9150, 9775, 10140, 10200,
13520, 8150, 8300, 9490, 9700, 10095, 10410, 10510, 10550, 10580,
10765, 12370, 14525, 9310, 11050, 14400, 15550, 15560, 15850, 15935,
16035, 16085, 16400, 16550, 16785, 18440, 18990, 18390, 12151, 12265,
12440, 12510, 12635, 12760, 12890, 13275, 13490, 13680, 13730, 13870,
14650, 15405, 16150, 16860, 18100, 12280, 12550, 12950, 13050, 13130,
13250, 13300, 13350, 13385, 13450, 13630, 13700, 13880, 13985, 14085,
14085, 14100, 14780, 14880, 14935, 15030, 15130, 15350, 15780, 21100,
15200, 15250, 15650, 15980, 16100, 16230, 16400, 16980, 17050, 17300,
19615, 15650, 8590, 10995, 11620, 12090, 9590, 10870, 11100, 11105, 11950,
13250, 15080, 15700, 16680, 17100, 18310, 15250, 10910, 14100, 14495, 14635,
16950, 12030, 12465, 12850, 12950, 13035, 13380, 13700, 14030, 14065, 14500,
14685, 14800, 17800, 7195, 7250, 7330, 7520, 7850, 8080, 8430, 9160, 9215, 10260,
11200, 8540, 8775, 8850, 9310, 9760, 11035, 11240, 12180, 14680, 10150, 10900, 11050, 11600,
11985, 12370, 12510, 12695, 12785, 12920, 13250, 13360, 13500, 13785, 13850, 13905,
13950, 14060, 14180, 14200, 14710, 14745, 14940, 15065, 15150, 15450, 15530, 15750,
15850, 16030, 16035, 16825, 18405, 11815, 12240, 12645, 13000, 13435, 13680, 13730,
13820, 13850, 14370, 14410, 14955, 15285, 15685, 16955, 12680, 13000, 13100, 13250,
13415, 13430, 14185, 16550, 15730, 16350, 16535, 16935, 17700, 17980, 19085, 24830,
6520, 6670, 6910, 7370, 8190, 9035, 9210, 9320, 11250, 11940, 8585, 8760, 8900,
8960, 9630, 9650,9725 ,10205 ,10520 ,10790, 11610, 12170, 13030, 12210, 12650, 13520,
13830, 13885, 14050, 14120, 14350, 14355, 15650, 16040, 16350, 16995, 17600, 18170, 11561,
12210, 12740, 12860, 13410, 13420, 13470, 13510, 13590, 13595, 13610, 13705, 15890, 12880,
13450, 14350, 16550, 16750, 17300, 17815, 4840, 6600, 7400, 7475, 7660, 8340, 8670, 8950, 10040,
10370, 7400, 8360, 8435, 10755, 10930, 9395, 13900, 11000, 11970, 11990, 12120, 12560, 12810, 13000,
13030, 13100, 7660, 8600, 8810, 8930, 9020, 9020, 9715, 9830, 10030, 10440, 7740, 8090, 9580, 10310,
10380, 11810, 10220, 10900, 11255, 10130, 12430, 12950, 13375,
13840, 14080, 14185, 14235, 14320,
14340, 15135, 15785, 15995, 16000, 16450, 16615, 16870, 17510, 17640, 18335, 18470, 19380, 12635,
15260, 12200, 12730, 13050, 15450, 15795, 16095, 16900, 15780, 15840, 11750, 12350, 12880, 13850, 14000,
15165, 19265, 5130, 7610, 8750, 9510, 9750, 9950 ,10210, 11620, 8360,8850, 9280, 10180, 12825, 12110, 15415,
14635, 16985, 17390, 16290, 12120, 12765, 12880, 13010, 13425, 14395, 15775, 16585, 12180, 13300, 13930,
15400,17080, 15320, 8960, 7655, 8760, 9510, 9750, 10125, 11835, 12160, 12500,
12920, 13300, 13305, 13385, 13400, 13450,13850, 13985, 14300,
14350, 14390, 14500, 14550, 14935, 15050, 15100, 15400, 15400, 15535, 15660, 15735, 16235,
17140, 17600, 17670, 17835, 17850, 18580, 19310, 14285, 15300, 15550,
11600, 12740, 12780, 12820, 13230, 14040, 14350,
14860, 15700, 16600, 21085, 12450, 12450, 12800, 12800,
12800, 12900, 12980, 13015, 13036, 13180, 13216, 13250, 13250,
14000, 19300, 19630, 15500, 16450, 16480, 18450, 18885, 26730, 5760)
alpha <- 0.1 # level of significance
n <- length(x)
x_bar <- mean(x) # sample mean
s <- sd(x) # sample standard deviation
mu <- 13500
t <- (x_bar-mu)/(s/sqrt(n))
p_value <-1-(pt(-t, n-1, lower.tail = TRUE)
-pt(t, n-1, lower.tail = TRUE))
print(x_bar)
print(n)
print(s)
print(t)
print(p_value)
if (p_value<alpha) {
"Reject Null Hypotheis"
} else {
"Do not Reject Null Hypotheis"
}

Ans

> print(x_bar)
13488.51
> print(n)
[ 599
> print(s)
3219.184
> print(t)
-0.0873358
> print(p_value)
0.9304338
> if (p_value<alpha) {
+ "Reject Null Hypotheis"
+ } else {
+ "Do not Reject Null Hypotheis"
+ }
"Do not Reject Null Hypotheis"

Conclusion : Since p_value < (0.10) we do not have sufficient evidence to reject Ho and we conclude that price =$13500