A physician wants to determine if a supplement is effective in helping men lose weight. She takes a random sample of overweight men and records their weights before the trial. She then prescribes the supplement and instructs them to take it for four weeks while making no other lifestyle changes. After the four-week period, she records the weights of the men again. Suppose that data were collected for a random sample of 6 men, where each difference is calculated by subtracting the weight before the trial from the weight after the trial. Assume that the weights are normally distributed.Identify the critical value of the t-test statistic for a left-tailed hypothesis test, where α=0.05. Probability0.100.050.0250.010.005Degrees of Freedom     51.4762.0152.5713.3654.03261.4401.9432.4473.1433.70771.4151.8952.3652.9983.49981.3971.8602.3062.8963.35591.3831.8332.2622.8213.250101.3721.8122.2282.7643.169111.3631.7962.2012.7183.106121.3561.7822.1792.6813.055131.3501.7712.1602.6503.012141.3451.7612.1452.6242.977151.3411.7532.1312.6022.947

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Asked Jun 18, 2019
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A physician wants to determine if a supplement is effective in helping men lose weight. She takes a random sample of overweight men and records their weights before the trial. She then prescribes the supplement and instructs them to take it for four weeks while making no other lifestyle changes. After the four-week period, she records the weights of the men again. Suppose that data were collected for a random sample of 6 men, where each difference is calculated by subtracting the weight before the trial from the weight after the trial. Assume that the weights are normally distributed.

Identify the critical value of the t-test statistic for a left-tailed hypothesis test, where α=0.05. 

Probability 0.10 0.05 0.025 0.01 0.005
Degrees of Freedom          
5 1.476 2.015 2.571 3.365 4.032
6 1.440 1.943 2.447 3.143 3.707
7 1.415 1.895 2.365 2.998 3.499
8 1.397 1.860 2.306 2.896 3.355
9 1.383 1.833 2.262 2.821 3.250
10 1.372 1.812 2.228 2.764 3.169
11 1.363 1.796 2.201 2.718 3.106
12 1.356 1.782 2.179 2.681 3.055
13 1.350 1.771 2.160 2.650 3.012
14 1.345 1.761 2.145 2.624 2.977
15 1.341 1.753 2.131 2.602 2.947
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Expert Answer

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Step 1

It is given that the sample size (n) is 6 and the hypothesized test is left- tailed. The level of significance (α) is 0.05.

The critical value for conducting the left-tailed test is the t-value, denoted –t(α, n-1).

Degrees of freedom:

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df n-1 -6-1 =5

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Step 2

Identifying the critical value from table:

Here, the degrees of freedom is 5 and the level of significance is 0.05.

  • Locate the value 5 in the degrees of freedom column.
  • Locate the 0.05 in the probability row.
  • The intersecting value that corresponds to 5 with level of significance 0.05 is 2.015.
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Probability Degrees of Freedom 0.10 0.05 0.025 0.01 0.005 1.4762.015 2.571 3.365||4.032 5 1.440 1.943 2.447 3.143||3.707 6 1.415 1.895 2.365 2.998 3.499 7 |1.397 1.860| |2.3062.896||3.355 8 |1.383 1.833| |2.262|2.821||3.250 1.372 1.812 2.228 | 2.764||3.169 10 1.363|1.796|2.201 2.718||3.106| 11 |1.356 |1.782|2.179 2.681 3.055 12 1.350 1.771 2.160 |2.650||3.012 |1.345 1.761 2.145 2.624||2.977 13 14 1.341 1.753 2.131 2.602| 2.947 15

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Step 3

Critical value:

The value obtained from table is 2.015.

Thus, the critical value for left-tailed t...

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Hypothesis Testing

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