Question

Conduct a hypothesis test using a two-tailed t test with an alpha level of .05.  You need to compare the hours/week spent on social media in two groups of 16 people (under and over age 25), with the M=8.5 and the SS= 68 for people under 25 and the M=6.5 and SS = 52 for people over 25 Is there a significant difference between them? If there is, which group spent more time on social media?

Answer 1

Given the following values (UNDER 25)

$\begin{gathered} \operatorname{mean}=\mu_1=8.5 \\ \text{standard deviation}=\sigma_1=68 \end{gathered}$

Given the following values ( OVER 25)

$\begin{gathered} \text{Mean =}\mu_2=6.5 \\ s\text{tandard deviation=}\sigma_2=52 \end{gathered}$

State the null and alternative hypothesis

$\begin{gathered} H_0;there\text{ is no significant difference betwe}en\text{ them} \\ H_a;\text{ there is a significant difference betw}een\text{ them} \end{gathered}$

State the significant level; alpha is 0.05

Calculate the statistical test

$t=\frac{\mu_1-\mu_2}{\sqrt[]{\frac{\sigma^2_1}{n_{}}+\frac{\sigma^2_2}{n_{}}}}$$\begin{gathered} \text{where n=16} \\ t=\frac{8.5-6.5}{\sqrt[]{\frac{68^2}{16}+\frac{52^2}{16}}} \end{gathered}$$t=\frac{2}{\sqrt[]{289+169}}=\frac{2}{\sqrt[]{458}}=\frac{2}{21.4}=0.093$

The degree of freedom is

$\begin{gathered} DF=n-2 \\ DF=16-2=14 \end{gathered}$

The P-value for the t-test score using a P-value calculator is 0.4636

Since the P-value is more than the alpha level, that is

$0.4636>0.05\text{ }$

Hence, the null hypothesis is accepted and there is no significant difference between them