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# Statistics and Hypothesis of Flammability Tests

1) Flammability tests were conducted on children's sleepwear. The vertical semi restrained test was used, in which pieces of fabric were burned under controlled conditions. After the burning stopped, the length of the charred portion was measured and recorded. The same fabric samples were tested at five different laboratories. The analysis of variance results are shown below:
Excel
Source of variation Ss Df Ms F P value F crit
Between groups 2.087194264 4 0.521798566 2.949333035 0.030665893 2.588834036
Within groups 7.607597403 43 0.17692087

Totals 9.694791667 47

A) What is the null hypothesis?
B) What is the alternative hypothesis?
C) Identify the value of the test statistic?
D) Find the critical value for a 0.05 significance level
E) Identify the P value
F) Is there sufficient evidence to support the claim that the means for the different laboratories are not all the same.

2) A randonm sample of 40 women is partitioned into three categories with ages of below 20, 20 through 40, and over 40. the analysis of variance results obtained from below:
Minitab
Source DF SS MS F P
Factor 2 938 469 1.65 0.205
Error 37 10484 283
Total 39 11422

A) What is the null hypothesis?
B) What is the alternative hypothesis?
C) Identify the value of the test statistic?
D) Identify the P value
E) Is there sufficient evidence to support the claim that women in the different age categories have different mean blood pressure levels.

3) The chest deceleration data (g) are given below. Use a 0.05 significance level to test the null hypothesis that the different weight categories have the same mean. Do the data suggest that larger cars are safer?

Subcompact 55 47 59 49 42
Compact 57 57 46 54 51
Midsize 45 53 49 51 46
Full size 44 45 39 58 44

4) A student of the author lives in a home with solar electric system. At the same time each day, she collected voltage readings from a meter connected to the system and the results are listed in the accompanying table. Use a 0.05 significance level to test the claim that the mean voltage reading is the same for the three different types of day. Is there sufficient evidence to support a claim of different population means? We might expect that a solar system would provide more electrical energy on sunny days than on cloudy or rainy days. Can we conclude that sunny days result in greater amounts of electrical energy?

Sunny Days Cloudy Days Rainy Days
13.5 12.7 12.1
13.0 12.5 12.2
13.2 12.6 12.3
13.9 12.7 11.9
13.8 13.0 11.6
14.0 13.0 12.2

5) The following table lists highway fuel consumption amounts (in mi/gal). Assume that fuel consumption amounts are not affected by an interaction between the type of transmission (manual or automatic) and the number of cylinders. Are fuel consumptions amounts affected by the type of transmission? Are fuel consumption amounts affected by the number of cylinders?

Cylinders
4 6 8
Manual 33 30 28
Automatic 31 27 24

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