During a time of national crisis, households in America follow internet news mor

Question

During a time of national crisis, households in America follow internet news more closely than they normally do. Assume that internet viewing times are normally distributed. A group analyzing the internet viewing habits during a recent crisis sampled 16 households and produced a mean viewing time for websites of 30.2 hours per week with a standard deviation of 16.4. Use this information to answer the following questions.

1.    If the research question is, "Do the data support the idea that the mean internet viewing time exceeds the mean of 21.18 hours per week that is typically observed in American households?" then the alternative hypothesis is a statement about the mean exceeding what value?

Explanation / Answer

let X denotes the internet viewing times in America

assumption is that X follows a normal distribution with mean=mu and variance=sigma2

1. we want to test whether the mean internet viewing time exceeds the mean of 21.18 hours per week that is typically observed in American households?

so null hypothesis H0:u=21.18 vs alternative hypothesis H1:u>21.18

to test this we have a sample of size n=16 with sample mean=xbar=30.2 and sample standard deviation=s=16.4

since the population variance is unknown it is estimated by s2

the test statistic is given as T=(Xbar-21.18)*sqrt(n)/s which under H0 follows a t distribution with df=n-1

since the alternative hypothesis is right tailed, H0 is rejected iff t>t0.05;n-1  where t is the observed value of T and t0.05;n-1 is the upper 0.05 point of a t distribution with df n-1

where 0.05 is the required level of significance.

now, t0.05;15=1.75305

and t=(30.2-21.18)*sqrt(16)/16.4=2.2

so t>t0.05;15

hence H0is rejectedat 5% level of significance and hence the data support the idea that the mean internet viewing time exceeds the mean of 21.18 hours per week that is typically observed in American households

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