Answered: eport states that adults 18- to 24- years-old send and receive 128 texts every day. Suppose we take a sample of 25- to 34- year-olds to see if their mean number…

A report states that adults 18- to 24- years-old send and receive 128 texts every day. Suppose we take a sample of 25- to 34- year-olds to see if their mean number of daily texts differs from the mean for 18- to 24- year-olds.

(a)

State the null and alternative hypotheses we should use to test whether the population mean daily number of texts for 25- to 34-year-olds differs from the population daily mean number of texts for 18- to 24-year-olds. (Enter != for ≠ as needed.)

H₀:

μ =128

H_a:

μ !=128

(b)

Suppose a sample of thirty 25- to 34-year-olds showed a sample mean of 118.4 texts per day. Assume a population standard deviation of 33.17 texts per day.

Compute the p-value. (Round your answer to four decimal places.)

p-value =

(c)

With

? = 0.05

as the level of significance, what is your conclusion?

Do not reject H₀. We cannot conclude that the population mean daily texts for 25- to 34-year-olds differs significantly from the population mean of 128 daily texts for 18- 24-year-olds.Reject H₀. We can conclude that the population mean daily texts for 25- to 34-year-olds differs significantly from the population mean of 128 daily texts for 18- 24-year-olds. Do not reject H₀. We can conclude that the population mean daily texts for 25- to 34-year-olds differs significantly from the population mean of 128 daily texts for 18- 24-year-olds.Reject H₀. We cannot conclude that the population mean daily texts for 25- to 34-year-olds differs significantly from the population mean of 128 daily texts for 18- 24-year-olds.

(d)

Repeat the preceding hypothesis test using the critical value approach.

State the null and alternative hypotheses. (Enter != for ≠ as needed.)

H₀:

μ = 128

H_a:

μ !=128

Find the value of the test statistic. (Round your answer to two decimal places.)

State the critical values for the rejection rule. (Use ? = 0.05. Round your answer to two decimal places. If the test is one-tailed, enter NONE for the unused tail.)

test statistic≤test statistic≥

State your conclusion.

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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