In an attempt to increase business on Monday nights, a restaurant offers free dessert with every dinner order. Before the offer, the mean number of dinner customers on Monday nights was 152. The following are the numbers of diners on a random sample of 12 Monday nights while the offer was in effect. 206 169 191 152 212 139 142 151 174 220 192 153

Dot plot. xlsx

Part (a) - 2 Points

Look at the above dot-plot of the data. Why does the plot suggest that it is okay to conduct a hypothesis test?

Part (b)

Test at the α = 0.05 level whether or not the dessert promotion increased the mean number of dinner customers on Monday nights.

After a dreary day of rain, the sun peeks through the clouds and a rainbow forms. you notice the rainbow is the shape of a parabola. the equation for this parabola is y = -x2 + 36. graph of a parabola opening down at the vertex 0 comma 36 crossing the x–axis at negative 6 comma 0 and 6 comma 0. in the distance, an airplane is taking off. as it ascends during take-off, it makes a slanted line that cuts through the rainbow at two points. create a table of at least four values for the function that includes two points of intersection between the airplane and the rainbow. analyze the two functions. answer the following reflection questions in complete sentences. what is the domain and range of the rainbow? explain what the domain and range represent. do all of the values make sense in this situation? why or why not? what are the x- and y-intercepts of the rainbow? explain what each intercept represents. is the linear function you created with your table positive or negative? explain. what are the solutions or solution to the system of equations created? explain what it or they represent. create your own piecewise function with at least two functions. explain, using complete sentences, the steps for graphing the function. graph the function by hand or using a graphing software of your choice (remember to submit the graph).