The accuracy of a coin-counter machine is gauged to accept nickels with a mean diameter of millimeters 21.21 mm. A sample of 36 nickles was drawn from a reported defective coin-counter machine located near a school. The sample had a sample mean of 21.215 mm and sample standard deviation 0.011 mm. Test the claim that the mean nickel diameter accepted by this coin-counter machine is greater than 21.21 mm. Test at the 0.1 significance level. (a) Identify the correct alternative hypothesis HaHa: μ<21.21μ<21.21 μ>21.21μ>21.21 μ=21.21μ=21.21 Give all answers correct to 4 decimal places. (b) The test statistic value is: (c) Using the Traditional method, the critical value is: (d) Based on your answers above, do you: Fail to reject H0H0 Reject H0
The accuracy of a coin-counter machine is gauged to accept nickels with a
Test the claim that the mean nickel diameter accepted by this coin-counter machine is greater than 21.21 mm. Test at the 0.1 significance level.
(a) Identify the correct alternative hypothesis HaHa:
- μ<21.21μ<21.21
- μ>21.21μ>21.21
- μ=21.21μ=21.21
Give all answers correct to 4 decimal places.
(b) The test statistic value is:
(c) Using the Traditional method, the critical value is:
(d) Based on your answers above, do you:
- Fail to reject H0H0
- Reject H0
From the given information,
Sample size n =36
the Sample mean, x̅ =21.215 mm
the Sample standard deviation, s=0.011 mm
the hypothesized mean, µ=21.21.
Degrees of freedom: 35(=36–1)
In this context, the population standard deviation is not known. It is appropriate to use t-test of a mean.
a)
The test hypotheses are given below:
Denote µ as the true mean
The Null hypothesis H0: µ =21.21 mm
The Alternative hypothesis H1: µ>21.21 mm.
The alternative hypothesis indicates a right-tailed test.
Therefore, the correct answer is “µ>21.21”.
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