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A watch manufacturer creates watch springs whose properties…

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A watch manufacturer creates watch...
A watch manufacturer creates watch springs whose properties must be consistent. In particular, the deviation in their weights must be no greater than 2.0 grams. Fifteen watch springs are selected from the production line and measured; their weights are 1, 4, 8, 7, 1, 5, 1, 5, 1, 4, 1, 4 ,3, 9, 1, 3 and grams. Assume a=0.01.

State the null and alternate hypotheses
Calculate the sample standard deviation
Determine which test statistic is appropiate (chi-square or F), and caluculate it's value.
Determine the critical value
State your decision: Should the null hypothesis be rejected?
Submitted: 8 years ago.Category: Math Homework
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Answered in 16 minutes by:
6/13/2010
Math Tutor or Teacher: abozer,
 replied 8 years ago
abozer
Category: Math Homework
Satisfied Customers: 6,159
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Hi again,

Could you please check the data. There are 16 data points where it is said to be 15.
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Customer reply replied 8 years ago
1, 4, 8, 7, 1, 5, 1, 4, 1, 4, 3, 9 1, 3 and 2 grams.
Math Tutor or Teacher: abozer,
 replied 8 years ago
Ho: σ ≤ 2.0
Ha: σ > 2.0

s = 2.667
n = 15

test statistic: chi-square = (n-1)(s/σ)^2 = (15-1)(2.667/2)^2 = 1.78

degree of freedom = 15 - 1 = 14

critical value: 29.14

We cannot reject the null hypothesis since the test statistic is not greater than the critical value.

We don't have sufficient information to conclude that the standard deviation in weights is greater than 2.0 grams.
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