1. A random sample of 64 customers at a drive-through bank window is observed, and it is found that the teller spends an average of 2.8 minutes with each customer, with a standard deviation of 1.2 minutes. Is there sufficient evidence to conclude that the teller spends less than 3 minutes with each customer slader

The degrees of freedom are given by:

The p value for this case would be given by:

If we use a significance level lower than 9% we have enough evidence to FAIL to reject the null hypothesis that the true mean is greater or equal than 3 but if we use a significance level higher than 9% the conclusion is oppossite we reject the null hypothesis

Step-by-step explanation:

Information given  

represent the sample mean

represent the standard deviation

sample size      

represent the value to verify

represent the significance level

t would represent the statistic (variable of interest)      

represent the p value

Hypothesis to verify

We want to check if the true mean for this case is less than 3 minutes, the system of hypothesis would be:      

Null hypothesis:      

Alternative hypothesis:      

The statistic for this case is given by:

(1)      

Replacing we got:

The degrees of freedom are given by:

The p value for this case would be given by:

If we use a significance level lower than 9% we have enough evidence to FAIL to reject the null hypothesis that the true mean is greater or equal than 3 but if we use a significance level higher than 9% the conclusion is oppossite we reject the null hypothesis

a - base

b - exponent

so,

answer: translate the circles so they share a common center point and dilate circle y by a scale factor of 3.