document.write( "Question 1182224: A seller claimed that her lip tint has a mean organic content of 90%. A rival seller asked 60 users of that lip tint and found that is has a mean organic content of 85% with a standard deviation of 5%. test the claim at 1% level of significance and assume that the population is approximately normally distributed. \n" ); document.write( "

Algebra.Com's Answer #812225 by Boreal(15235) $\"\"$ $\"About$

You can put this solution on YOUR website!
Despite the proportion, this is not a 1-sample proportion test but a 1-sample t-test. The mean is presumably the mean of the percentages, rather than the percent 90% or more.
\n" ); document.write( "Ho: mu=90%
\n" ); document.write( "Ha: mu NE 90%
\n" ); document.write( "alpha=0.01 p{reject Ho|Ho true}
\n" ); document.write( "test is a t(0.995, df=59)
\n" ); document.write( "critical value is |t|>2.664
\n" ); document.write( "calculation t=(85-90)/5/sqrt(60)
\n" ); document.write( "=-5*sqrt(60)/5
\n" ); document.write( "=-7.75
\n" ); document.write( "reject Ho, the mean is not 90%, p-value about 1 x 10^-10
\n" ); document.write( " \n" ); document.write( "

\n" );