Question

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:

  

H_a:

   Your answer cannot be understood or graded. More Information

(b)

Suppose a sample of thirty 25- to 34-year-olds showed a sample mean of 118.7 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

α = 0.05

as the level of significance, what is your conclusion?

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.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.

(d)

Repeat the preceding hypothesis test using the critical value approach.

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

H₀:

128

  

H_a:

   

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

State the critical values for the rejection rule. (Use α = 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.

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.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.

Answer 1

Answer:

a)

H0: u = 128

Ha: u != 128

b)

Standard error SE = s/sqrt(n)

substitute values

= 33.17/sqrt(30)

= 6.0560

Test statistic z = (x-u)/(s/sqrt(n))

Z = (118.9 - 128)/6.0560

= - 1.5026

Table of Area Under Standard Normal Curve gives region = 0.4332

Along these lines,

p-esteem = (0.5 - 0.4332) * 2

= 0.0668*2

= 0.1336

c)

Since p - esteem = 0.1335 is more noteworthy than alpha = 0.05, the thing that matters isn't critical. Neglect to dismiss Ho

End:

The information don't bolster the case that their mean number of every day writings contrasts from the mean for 18-to 24-year-olds.

d)

H0: u = 128

Ha: u != 128

Standard error = s/sqrt(n)

substitute values

= 33.17/sqrt(30)

z = 6.0560

Test Statistic z = (x - u)/se

substitute values

= (118.9 - 128)/6.0560

= - 1.50

alpha = 0.05

From Table, basic estimations of Z = 1.96.

Here we observe that, test statistic > Critical value

Since determined estimation of z = - 1.50 is more noteworthy than basic estimation of z = - 1.96, the thing that matters isn't critical.

Neglect to dismiss Ho.

End:

The information don't bolster the case that their mean number of every day writings contrasts from the mean for 18-to 24-year-olds.

f)

Right alternative:

Try not to dismiss Ho.

We can't presume that the populace mean day by day messages for 25-to 34-year-olds varies fundamentally from the populace mean of 128 day by day messages for 18-24-year-olds.