Assume the samples are random and independent, the populations are normally distributed, and the population variances are equal. The table available below shows the prices (in dollars) for a sample of automobile batteries. The prices are classified according to battery type. At α=0.10, is there enough evidence to conclude that at least one mean battery price is different from the others? Complete parts (a) through (e) below.
Transcribed Image Text:i
Cost of batteries by type
Group size 35
Group size 65
Group size 24/24F
100| 111
144| 177
90
121
124
178 282
140 | 140
89
79
84
125
Print
Done
Transcribed Image Text:Assume the samples are random and independent, the populations are normally distributed, and the population variances are equal. The table available below shows the prices (in dollars) for a sample of automobile
batteries. The prices are classified according to battery type. At a = 0.10, is there enough evidence to conclude that at least one mean battery price is different from the others? Complete parts (a) through (e) below.
Click the icon to view the battery cost data.
(a) Let u1, 42, H3 represent the mean prices for the group size 35, 65, and 24/24F respectively. Identify the claim and state Ho and Ha.
Ho:
Ha:
The claim is the
hypothesis.
(b) Find the critical value, Fo, and identify the rejection region.
The rejection region is F
V Fo, where Fo
%3D
(Round to two decimal places as needed.)
(c) Find the test statistic F.
F =
(Round to two decimal places as needed.)
(d) Decide whether to reject or fail to reject the null hypothesis.
Ho because the test statistic
V in the rejection region.
(e) Interpret the decision in the context of the original claim.
There
V enough evidence at the
% level of significance to
V the claim that
mean battery price is
the others.
(Type an integer or a decimal.)
Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...
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