A manufacturer claims that the calling range (in feet) of its 900-MHz cordless telephone is greater than that of its leading competitor. A sample of 1313 phones from the manufacturer had a mean range of 10901090 feet with a standard deviation of 2121 feet. A sample of 99 similar phones from its competitor had a mean range of 10301030 feet with a standard deviation of 4242 feet. Do the results support the manufacturer's claim? Let μ1�1 be the true mean range of the manufacturer's cordless telephone and μ2�2 be the true mean range of the competitor's cordless telephone. Use a significance level of α=0.05�=0.05 for the test. Assume that the population variances are equal and that the two populations are normally distributed.
Step 2 of 4 :
Compute the value of the t test statistic. Round your answer to three decimal places.
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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Step 1: Determine the given data
VIEWStep 2: Make hypotheses
VIEWStep 3: Calculate the value of the t test statistic
VIEWStep 4: Obtain decision rule for rejecting the null hypothesis H0
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