Foot-Length: It has been claimed that, on average, right-handed people have a le
ID: 2932097 • Letter: F
Question
Foot-Length: It has been claimed that, on average, right-handed people have a left foot that is larger than the right foot. Here we test this dlaim on a sample of 10 right- handed adults. The table below gives the left and right foot measurements in millimeters (mm). Test the claim at the 0.01 significance level. You may assune the sample o differences comes from a normally distributed population. Person Left Foot (x) Right Foot (v) difference (d-x-y) 270 265 259 252 256 271 268 254 270 251 270 267 253 259 271 272 56 253 Mean 262.90 7.99 30 8.04 If you are using software, you should be able copy and paste the data directly into your software program (a) The claim is that the mean difference is positive (e0). What type of test is this? This is a right-tailed test. 0 This is a two-tailed test. O This is a left-tailed test. (b) What is the test statistic? Round your answer to 2 decimal places. To account for hand calculationsv software, your answer must be within 0.01 of the true answer (c) Use software to get the P-value of the test statistic. Round to 4 decimal places P-value (d) What is the conclusion regarding the null hypothesis? 0 reject He O fail to reject Ho (e) Choose the appropriate concluding statement -The data supports the claim that, on average, right-handed people have a left foot that is larger than the right foot. Thare is not enough data to support the claim that, on average, right-handed people have a left foot that is larger than the right foot. o We reject the claim that, on average, riohe handed people have a len foot that in arger than the right fosot O we have proven that, on average, right-handed people have a left foot that is larger than the right foot.Explanation / Answer
a) Here we are trying to see whether the left foot of right handed people is larger than their right foot.
Since thr rejection region is only in one tail on the right side, so it right tailed test.
b) test statistic can be calculated using the below formula:
(observed - expected)/SE
Here SE = sd/sqrt(n) = 1.70/sqrt(10) = 0.5375872
So test statistic = (1.30 - 0)/0.5375872 = 2.418212
c) Here degrees of freedom = 10 - 1 = 9
Now we can look at the t table to find the correspoding p value.
p value is (1 - 0.9806) = 0.0194
d) Since p value 0.0194 is greater than 0.01, we fail to reject the null hypothesis.
So second option is correct.
e) Second option is correct. i.e. there is not enough data to support the claim that, on average, right handed people have a left foot that is larger than the right foot.