Researchers were interested in the amount of time children spend on social media

Question

Researchers were interested in the amount of time children spend on social media. The National Longitudinal Survey of Children and Youth reported that in 2012 children in the 6 to 10 age group spent an average of 12 hours per week on social media. The researchers hypothesized that childiren in 2017 spend more time on social media. They surveyed 13 children in the 6 to 10 age group and the res were analyzed with SPSS, interpret the SPSS output obtained. What conclusion can the researchers draw? Write a summary sentence of the results T-TEST ONE-SAMPLE STATISTICS Standard error Deviation Mean mean IN 15.6923 55585s Score 13 1.54166 One-Sample Test Test Value -12 95% confidence interval of the Sig. (2-tailed) Mean difference 2.395 12 034 3.69231 .0513 SCORE

Explanation / Answer

From the table 1

sample size n=13

mean of sample = sum(xi)/n =15.6923

The sample mean is 15.6923 hours.

sd of the sample = sum((xi-xbar)^2)/(n-1)=5.55855

se of mean = sd/sqrt(13) =1.54166

Null hypothesis H0: mu=12

Alternative hypothesis H1: mu>12

t stat = (xbar-mu)/se =(15.6923-12)/1.54166 =2.395

df = n-1 =12

mean difference = xbar - mu = 3.6923

tcritcal = 2.179 (alpha=.05,df=12)

95% CI is

meandifference +/ - tcritical * se = 3.6923 +/- 2.179 * 1.54166 =(.333, 7.051)

Lowe CI = 0.333

Upper CI = 7.051

Significance (2 tailed) = 2*P(t>2.395)=2* 0.0169 = 0.034

Significance (1 tailed) = P(t>2.395)=0.0169

The pvalue one tail is 0.0169 which is less than 0.05. We reject the null hypothesis that mu=12.

It can be concluded that there is a significant increase in the amount of time children (age group 6-10) spend on social media from 2012 to 2017 with 5% level of significance.

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