A company manufactures tennis balls. When its tennis balls are dropped onto a concrete surface from a height of 100 inches, the company wants the mean height the balls bounce upward to be 54.8 inches. This average is maintained by periodically testing random samples of 25 tennis balls. If the t-value falls between −t0.98 and t0.98, then the company will be satisfied that it is manufacturing acceptable tennis balls. A sample of 25 balls is randomly selected and tested. The mean bounce height of the sample is 56.6 inches and the standard deviation is 0.25 inch. Assume the bounce heights are approximately normally distributed. Is the company making acceptable tennis balls? Find −t0.98 and t0.98.−t0.98 = t0.98=Find the t-value Table 5-t-DistributionLevel ofconfidence, cd.f.123456789101112131415161718192021222324252627282930313233343536373839404550607080901005001000One tail, aTwo tails, a0.800.900.100.050.200.103.0786.3141.886 2.9201.6382.3531.5332.1321.476 2.0150.95 0.980.990.025 0.01 0.0050.05 0.020.0112.706 31.821 63.6574.303 6.9659.9253.182 4.5415.8412.776 3.7474.6042.5713.3654.0323.1432.4473.7072.9983.4992.8963.3552.8213.2503.1693.1062.681 3.0553.0122.9771.4401.9431.415 1.8951.397 1.8601.383 1.8331.372 1.8121.3631.7961.356 1.7821.3502.160 2.6501.7711.345 1.761 2.1452.6241.341 1.7532.1312.6021.337 1.746 2.120 2.5831.333 1.7402.1102.5671.3301.7342.1012.5521.328 1.7292.093 2.5391.325 1.7252.0862.5281.323 1.721 2.0802.518 2.8311.321 1.7172.0742.508 2.8191.319 1.7142.0692.5002.8071.3181.711 2.064 2.4922.7971.316 1.708 2.0602.4852.7871.315 1.7062.0562.4792.7791.314 1.7032.0522.4732.7711.3131.7012.0482.4672.7631.311 1.6992.045 2.462 2.7561.310 1.6972.7502.042 2.4572.4532.0401.3091.6962.7441.309 1.6942.037 2.449 2.7381.308 1.6922.4452.0351.307 1.691 2.032 2.4412.7241.306 1.6902.4382.0301.306 1.688 2.028 2.4342.7191.305 1.687 2.0262.4312.7151.3041.686 2.024 2.4292.7121.3041.685 2.023 2.426 2.7081.3032.7041.684 2.021 2.4231.301 1.679 2.014 2.4122.6901.299 1.676 2.009 2.403 2.6781.296 1.671 2.000 2.390 2.6601.994 2.381 2.6481.990 2.374 2.6392.6321.2941.6671.292 1.6641.2911.6621.987 2.3681.290 1.6601.984 2.3642.6261.283 1.648 1.965 2.334 2.5861.282 1.646 1.962 2.330 2.5811.282 1.645 1.960 2.326 2.5762.3652.3062.2622.2282.7642.201 2.7182.1792.9472.9212.8982.8782.8612.8452.7332.728c-confidence intervalα-1Left-tailed testRight-tailed testTwo-tailed testrat

From given data we have ; Sample mean x=56.6 Sample standard deviation s=0.25 sample size n=25…

Answered: A company manufactures tennis balls.…

Holt Mcdougal Larson Pre-algebra: Student Edition 2012

1st Edition

ISBN:9780547587776

Author:HOLT MCDOUGAL

Publisher:HOLT MCDOUGAL

Chapter11: Data Analysis And Probability

Section11.1: Stem-and-leaf Plots And Histograms

Problem 10E

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A company manufactures tennis balls. When its tennis balls are dropped onto a concrete surface from a height of 100 inches, the company wants the mean height the balls bounce upward to be 54.8 inches. This average is maintained by periodically testing random samples of 25 tennis balls. If the t-value falls between −t0.98 and t0.98, then the company will be satisfied that it is manufacturing acceptable tennis balls. A sample of 25 balls is randomly selected and tested. The mean bounce height of the sample is 56.6 inches and the standard deviation is 0.25 inch. Assume the bounce heights are approximately normally distributed. Is the company making acceptable tennis balls?

Find −t0.98 and t0.98.

−t0.98 =

t0.98=

Find the t-value

Table 5-t-Distribution
Level of
confidence, c
d.f.
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
45
50
60
70
80
90
100
500
1000
One tail, a
Two tails, a
0.80
0.90
0.10
0.05
0.20
0.10
3.078
6.314
1.886 2.920
1.638
2.353
1.533
2.132
1.476 2.015
0.95 0.98
0.99
0.025 0.01 0.005
0.05 0.02
0.01
12.706 31.821 63.657
4.303 6.965
9.925
3.182 4.541
5.841
2.776 3.747
4.604
2.571
3.365
4.032
3.143
2.447
3.707
2.998
3.499
2.896
3.355
2.821
3.250
3.169
3.106
2.681 3.055
3.012
2.977
1.440
1.943
1.415 1.895
1.397 1.860
1.383 1.833
1.372 1.812
1.363
1.796
1.356 1.782
1.350
2.160 2.650
1.771
1.345 1.761 2.145
2.624
1.341 1.753
2.131
2.602
1.337 1.746 2.120 2.583
1.333 1.740
2.110
2.567
1.330
1.734
2.101
2.552
1.328 1.729
2.093 2.539
1.325 1.725
2.086
2.528
1.323 1.721 2.080
2.518 2.831
1.321 1.717
2.074
2.508 2.819
1.319 1.714
2.069
2.500
2.807
1.318
1.711 2.064 2.492
2.797
1.316 1.708 2.060
2.485
2.787
1.315 1.706
2.056
2.479
2.779
1.314 1.703
2.052
2.473
2.771
1.313
1.701
2.048
2.467
2.763
1.311 1.699
2.045 2.462 2.756
1.310 1.697
2.750
2.042 2.457
2.453
2.040
1.309
1.696
2.744
1.309 1.694
2.037 2.449 2.738
1.308 1.692
2.445
2.035
1.307 1.691 2.032 2.441
2.724
1.306 1.690
2.438
2.030
1.306 1.688 2.028 2.434
2.719
1.305 1.687 2.026
2.431
2.715
1.304
1.686 2.024 2.429
2.712
1.304
1.685 2.023 2.426 2.708
1.303
2.704
1.684 2.021 2.423
1.301 1.679 2.014 2.412
2.690
1.299 1.676 2.009 2.403 2.678
1.296 1.671 2.000 2.390 2.660
1.994 2.381 2.648
1.990 2.374 2.639
2.632
1.294
1.667
1.292 1.664
1.291
1.662
1.987 2.368
1.290 1.660
1.984 2.364
2.626
1.283 1.648 1.965 2.334 2.586
1.282 1.646 1.962 2.330 2.581
1.282 1.645 1.960 2.326 2.576
2.365
2.306
2.262
2.228
2.764
2.201 2.718
2.179
2.947
2.921
2.898
2.878
2.861
2.845
2.733
2.728
c-confidence interval
α
-1
Left-tailed test
Right-tailed test
Two-tailed test
r
a
t

Features Features Normal distribution is characterized by two parameters, mean (µ) and standard deviation (σ). When graphed, the mean represents the center of the bell curve and the graph is perfectly symmetric about the center. The mean, median, and mode are all equal for a normal distribution. The standard deviation measures the data's spread from the center. The higher the standard deviation, the more the data is spread out and the flatter the bell curve looks. Variance is another commonly used measure of the spread of the distribution and is equal to the square of the standard deviation.

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