A fast-food chain claims one medium order of its onion rings weighs 114 grams. Patrice thinks she is getting less than what the restaurant advertises. She weighs the next 16 random orders of onion rings before she eats them and finds the sample mean is 112.4 grams and the standard deviation is 7.63 grams. What conclusion can be drawn α = 0.10?

There is not any solid evidence provided by Patrice to reject the fast food chain's claim.

Step-by-step explanation:

As Patrice weighs the next 16 random orders of onion rings before she eats them and finds the sample mean is 112.4 grams and the standard deviation is 7.63 grams so here

sample size = 16

sample mean = 112.4

standard deviation = 7.63

Formula for test statistic:

t = ( sample mean - weight ) / standard error of mean

Formula for standard error of mean:

standard error of mean =  standard deviation / sqrt (sample size)

therefore by putting the values in the above formula, we get

standard error of mean = 7.63 / sqrt(16)

Now

t = ( 112.4-114 ) / ( 7.63 / sqrt(16) )

= -0.84

p-value = P (z < -0.84) = 0.201

Therefore it fails to reject null hypothesis because p-value > 0.1

Hence, there is not any solid evidence provided by Patrice to reject the fast food chain's claim.

- "runner b is moving at a slower rate."

- "the graphs shown are graphs of distance(km) against time(min).

the slopes of this graphs are are given by:

slope = (change in y)/(change in x)

= (change in distance)/(change in time)

this is the formula for finding the speed. so, the slope of these graphs represent the speed of the runner.

taking each division in the graph to represent 1 on both axis:

runner a ⇒ speed = (2-0)/(1-0)

= 2/1

= 2 km/min

runner b ⇒ speed = (3-0)/(3-0)

= 3/3

= 1 km/min

this shows that   runner b is moving at a slower rate."