A researcher want to determine if there is a linear...

A researcher want to determine if there is a linear relationship between the number of hours a person goes without sleep (x) and the number of mistakes he makes on a simple test (y) the following data are recorded. n=6,

Transcript

00:01 Question we are given here researcher so here we are given here that researcher wants researcher want to see the relationship between number of hours we can write numbers of hours of numbers of hours a person study person studied this is the person of we can denote by x and number of points they earn on a sort this here we can write number of points they on our points they and on a sort taste on sort taste which is denoted by y so here level significance we are given a 0.

01:00 0 1 so here we can write the whole whole study and the number of points x and y is we are given data we are given here so let's solve this question so first let's let us find out the h node is a nice null hypothesis so we can write r which is equal to zero versus we can write h1 here we can write r not equal to zero now in the b we can be given here critical region of obtaining a t distribution so here we'll last talk about critical region critical region the obtain is using a t distribution right t distribution at one person level here we can write 1 % level of significance level of significance and with n minus 1 which is equal to n minus 2 so here we can write 5 minus 2 which is equal to 3 so here we can write 5 minus 2 which is equal to 3 and the d f which is equal to we can write 4 .541 now in the third we are given a under the null hypothesis so in the null hypothesis we are given here t statistics t which is equal we can write r multiple by we can write n minus 2 divided by we can write 1 minus r square so this is the formula of calculation of the r so let's find out the value of r so we can write r which is equal to summation of x minus x bar and here we can write y minus y bar divided by we can write we can score out of sigma of x minus x bar square and summation of we can write y minus y bar square so this value we are given here and we can write r which is equal to 22 divided by we can write score root of 30 multiple by 22 we just simplify we can write here answer is 0 .85 64 64 and here we can write t statistic t which is equal we can write 0 .8565 multiple we can write it's got root of 3 divided by 0 .2667.

03:24 We just simplify and we can write here answer is 2 .8723.

03:29 This is the correct answer.

03:32 And here, let's try the table...

Question

A researcher want to determine if there is a linear relationship between the number of hours a person goes without sleep (x) and the number of mistakes he makes on a simple test (y) the following data are recorded. n=6,

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