A political analyst believes that a senator's recent decision to support a bill resulted in a drop of approval ratings. To test thisclaim, he selects random cities in the state that voted the senator in and compares the approval ratings before the decisiornto the approval ratings after the decision. Suppose that data were collected for a random sample of 8 cities, where eachdifference is calculated by subtracting the percent approval rating before the decision from the percent approval rating afterthe decision. Assume that the percentages are normally distributed. Identify the critical value(s) of the t-test statistic, whereα-0.05. Use a comma and a space to separate answers as needed0.01ProbabilityDegrees of Freedom560.100.050.0250.0051.4761.4401.4151.3971.3831.3721.3631.3561.3501.3451.3412.0151.9431.8951.8601.8331.8121.7961.7822.5712.4472.3652.3062.2622.2282.2012.1792.1602.1452.1313.3653.1432.9982.8962.8212.7642.7182.6812.6502.6242.6024.0323.7073.4993.3553.2503.1693.1063.0553.0122.9772.9471.7611.753

Question
Asked Apr 12, 2019

Critical Values= 

A political analyst believes that a senator's recent decision to support a bill resulted in a drop of approval ratings. To test this
claim, he selects random cities in the state that voted the senator in and compares the approval ratings before the decisiorn
to the approval ratings after the decision. Suppose that data were collected for a random sample of 8 cities, where each
difference is calculated by subtracting the percent approval rating before the decision from the percent approval rating after
the decision. Assume that the percentages are normally distributed. Identify the critical value(s) of the t-test statistic, where
α-0.05. Use a comma and a space to separate answers as needed
0.01
Probability
Degrees of Freedom
5
6
0.10
0.05
0.025
0.005
1.476
1.440
1.415
1.397
1.383
1.372
1.363
1.356
1.350
1.345
1.341
2.015
1.943
1.895
1.860
1.833
1.812
1.796
1.782
2.571
2.447
2.365
2.306
2.262
2.228
2.201
2.179
2.160
2.145
2.131
3.365
3.143
2.998
2.896
2.821
2.764
2.718
2.681
2.650
2.624
2.602
4.032
3.707
3.499
3.355
3.250
3.169
3.106
3.055
3.012
2.977
2.947
1.761
1.753
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A political analyst believes that a senator's recent decision to support a bill resulted in a drop of approval ratings. To test this claim, he selects random cities in the state that voted the senator in and compares the approval ratings before the decisiorn to the approval ratings after the decision. Suppose that data were collected for a random sample of 8 cities, where each difference is calculated by subtracting the percent approval rating before the decision from the percent approval rating after the decision. Assume that the percentages are normally distributed. Identify the critical value(s) of the t-test statistic, where α-0.05. Use a comma and a space to separate answers as needed 0.01 Probability Degrees of Freedom 5 6 0.10 0.05 0.025 0.005 1.476 1.440 1.415 1.397 1.383 1.372 1.363 1.356 1.350 1.345 1.341 2.015 1.943 1.895 1.860 1.833 1.812 1.796 1.782 2.571 2.447 2.365 2.306 2.262 2.228 2.201 2.179 2.160 2.145 2.131 3.365 3.143 2.998 2.896 2.821 2.764 2.718 2.681 2.650 2.624 2.602 4.032 3.707 3.499 3.355 3.250 3.169 3.106 3.055 3.012 2.977 2.947 1.761 1.753

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Expert Answer

Step 1

Obtain the critical value in case of right tailed hypothesis test

Here, it is given that the percentage values are normally distributed and the population standard deviation is unknown.

The sample size is n = 8.

The claim is that there is drop in the approval rate.

For testing the claim, here a sample of size n =8 was collected. The data is paired data.

Let the mean difference d-bar is the average of the differences.

Hypothesis:

 

Therefore the test is a right tailed test.

The critical value corresponding to right tailed test is obtained as 1.895 from the calculation given below:

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Step 2

Obtain the critical value in case of two tailed hypothesis test:

Here, it is given that the percentage values are normally distributed and the population standard deviation is unknown.

The sample size is n = 8.

From the...

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