Conduct a hypothesis test determine if the average time a student can balance on 1 foot is different than the guest in question one
Added by Glenn U.
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\(H_0: \mu = \mu_0\) - Alternative hypothesis \(H_a\): The average time a student can balance on one foot is different from the guest's average time. \(H_a: \mu \neq \mu_0\) (Here, \(\mu_0\) is the guest's average time from question one.) --- Show more…
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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 claim 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 0.05 significance level. You may assume the sample of differences comes from a normally distributed population. Person Left Foot (x) Right Foot (y) difference (d = x − y) 1 274 273 1 2 269 268 1 3 260 262 -2 4 256 255 1 5 262 259 3 6 274 274 0 7 273 271 2 8 259 257 2 9 274 273 1 10 256 254 2 Mean 265.70 264.60 1.10 s 7.82 8.04 1.37 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 (μd > 0). What type of test is this? This is a left-tailed test. This is a right-tailed test. This is a two-tailed test. (b) What is the test statistic? Round your answer to 2 decimal places. t d = To account for hand calculations -vs- 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? reject H0 fail to reject H0 (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. 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. We reject the claim that, on average, right-handed people have a left foot that is larger than the right foot. We have proven that, on average, right-handed people have a left foot that is larger than the right foot.
Adi S.
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 claim 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 assume the sample of differences comes from a normally distributed population. Person Left Foot (x) Right Foot (y) 1 273 272 2 268 267 3 259 261 4 255 254 5 261 258 6 273 273 7 273 270 8 258 256 9 273 272 10 255 253 You should be able copy and paste the data directly into your software program. (a) The claim is that the mean difference (x - y) is positive (μd > 0). What type of test is this? This is a two-tailed test. This is a left-tailed test. This is a right-tailed test. (b) What is the test statistic? Round your answer to 2 decimal places. td = (c) What is the P-value of the test statistic? Round to 4 decimal places. P-value = (d) What is the conclusion regarding the null hypothesis? reject H0 fail to reject H0 (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. 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. We reject the claim that, on average, right-handed people have a left foot that is larger than the right foot.
1. Testing paired differences A graduate student is interested in how viewing different kinds of scenery affects working memory. For his study, he selects a random sample of 49 adults. The subjects complete a test of working memory before and after walking in a nature setting. Before the walk, the mean score on the test of working memory was 9.4. After the walk, the mean score was 8.5. The mean of the differences between each person's pre- and post- scores was 0.9, with a standard deviation of the differences equal to 1.8. The graduate student has no presupposed assumptions about how viewing different kinds of scenery affects working memory, so he formulates the null and alternative hypotheses as: H0: μd = 0 H1: μd ≠ 0 He uses a repeated-measures t test. Because the sample size is large, if the null hypothesis is true, the test statistic follows a t-distribution with n - 1 = 49 - 1 = 48 degrees of freedom. Use the Distributions tool to find the critical region for α = .05. The critical t values, which form the boundaries of the critical region, are __________ . The test statistic is t = __________ . Use the tool to evaluate the null hypothesis. (Note: You can place the purple line on your t-statistic to tell whether it lies within or outside the critical region. It's possible that this line may not rest exactly on the t-statistic, but you will be able to tell whether it lies within or outside the critical region.) The t-statistic __________ in the critical region for a two-tailed hypothesis test. Therefore, the null hypothesis is __________ . The graduate student __________ conclude that viewing nature scenery affects working memory.
David N.
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