Alocal eat-in pizza restaurant wants to investigate the possibility of starting to deliver pizzas. the owner of the store has determined that home delivery will be successful if the average time spent on the deliveries does not exceed 36 minutes. the owner has randomly selected 20 customers and has delivered pizzas to their homes in order to test if the mean delivery time actually exceeds 36 minutes. suppose the p-value for the test was found to be 0.0275. state the correct conclusion.

a. at α=0.05, we fail to reject h0.
b. at α=0.02, we reject h0.
c. at α=0.03, we fail to reject h0.
d. at α=0.025, we fail to reject h0.

d) At α=0.025, we fail to reject H0.

True. Since the p value is higher than the significance level 0.0275>0.025 we have enough evidence to FAIL to reject the null hypothesis.

Step-by-step explanation:

1) Data given and notation    

represent the sample mean  

represent the sample standard deviation    

sample size    

represent the value that we want to test  

represent the significance level for the hypothesis test.    

t would represent the statistic (variable of interest)    

represent the p value for the test  

2) State the null and alternative hypotheses.    

We need to conduct a hypothesis in order to check if the mean is higher than 36 minutes :    

Null hypothesis:    

Alternative hypothesis:    

Since we don't know the population deviation, is better apply a t test to compare the actual mean to the reference value, and the statistic is given by:    

(1)    

t-test: "Is used to compare group means. Is one of the most common tests and is used to determine if the mean is (higher, less or not equal) to an specified value".    

3) Calculate the statistic    

We don't have info provided to calculate it but we can assume that is    

4) P-value    

First we need to calculate the degrees of freedom given by:

Since is a right tailed test the p value would be:    

5) Conclusion    

a) At α=0.05, we fail to reject H0.

False. On this case since the p value is lower than the significance level 0.0275<0.05 we have enough evidence to reject the null hypothesis not the opposite.

b) At α=0.02, we reject H0.

False. Since the p value is higher than the significance level because 0.0275>0.02 we FAIL to reject the null hypothesis not the opposite.

c)  At α=0.03, we fail to reject H0.

False, since the p value is lower than the significance level because 0.0275<0.03 we have enough evidence to reject the null hypothesis not the opposite.

d) At α=0.025, we fail to reject H0.

True. Since the p value is higher than the significance level 0.0275>0.025 we have enough evidence to FAIL to reject the null hypothesis.

intensity of the vector is v= √37 ≈ 6.08 units and make angle ∡α ≈ 9.46° with east direction

step-by-step explanation:

required vector is consists of the two componentsvx= 2+4=6 units   and vy= 1 unit and vx ⊥ vywe will use pythagorian theorem to find intensity of the vector vv∧2 = vx∧2 + vy∧2 => v = √vx∧2 + vy∧2 = √6∧2 + 1∧2 = √36+1 = √37 ≈ 6.08 unitsthe angle ∡α between vector and east direction we wil find with tanαtanα = 1/6 => α = arc tanα = arc 1/6 => α ≈ 9.46°

hope this

2 & 7

step-by-step explanation:

he climbs 300 ft/hr at a constant rate. the peak is at 1,500 ft.

when going up, he reaches 600 ft in 2 hours. remember, that he is going in a constant rate. divide 600 with 300:

600/300 = 2

assuming that he takes the same route back (meaning that it's a 1500 ft route back, you can solve.

note also that you are solving when he gets back to 600 ft after he reaches the peak.

first, find the amount of hours it takes to get up the peak. divide the total amount (1500), with the ft/her (300) to get the amount of hours (x):

1500/300 = x

x = 5

it takes jamie 5 hours to get up. now, he is returning down, and reaches 600 (his current destination). remember that he climbs at a constant 300 ft/hr. divide 600 with 300:

600/300 = x

x = 2

now add the two numbers together.

x = 5 + 2 = 7

jamie takes 7 hours to go up the mountain and reach his current position when descending.

(total amount/constant rate) = (time).

remember that it is a constant rate, so in total, when he gets back down the mountain, it will take the same amount of time as when he goes up. the total amount for the round trip is: 5 + 5 = 10.

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