Adigital camcorder repair service has set a goal not to exceed an average of 5 working days from the time the unit is brought in to the time repairs are completed. a random sample of 12 repair records showed the following repair times (in days): 9, 2, 5, 1, 5, 4, 7, 5, 11, 3, 7, 2. click here for the excel data file (a) h0: μ ≤ 5 days versus h1: μ > 5 days. at α = .05, choose the right option. reject h0 if tcalc > 1.796 reject h0 if tcalc < 1.796 a bcalculate the test statistic.

(c-1) the null hypothesis should be rejected.

true
false
(c-2) the average repair time is longer than 5 days.

true
false
(c-3) at \alpha = .05 is the goal being met?

yes
no

c-1) The null hypothesis should be rejected.

FALSE

c-2) The average repair time is longer than 5 days.

FALSE

c-3) At \alpha = .05 is the goal being met?

YES we fail to reject the null hypothesis

Step-by-step explanation:

Data given and notation  

represent the mean for the sample  

represent the sample standard deviation for the sample  

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 (variable of interest)  

State the null and alternative hypotheses.  

We need to conduct a hypothesis in order to check if the mean is actually higher than 5, the system of hypothesis would be:  

Null hypothesis:  

Alternative hypothesis:  

If we analyze the size for the sample is > 30 but we don't know the population deviation so 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".  

Calculate the statistic

We can replace in formula (1) the info given like this:  

P-value

The first step is calculate the degrees of freedom, on this case:  

Since is a one side test the p value would be:  

Conclusion  

If we compare the p value and the significance level given we see that so we can conclude that we have enough evidence to FAIL reject the null hypothesis, so we can conclude that the population mean is not significantly higher than 5.  

c-1) The null hypothesis should be rejected.

FALSE

c-2) The average repair time is longer than 5 days.

FALSE

c-3) At \alpha = .05 is the goal being met?

YES we fail to reject the null hypothesis

solution:

as, mean is defined as sum of all the observations divided by total number of observations.

and , median is mid value of the data whether arranged in ascending order or descending order.

consider, roadsters:

2,3,4,5,6,7,8,9

mean =

also, median= , because number of observations is even, so median is mean of two mid values.

now, coming to bandits

2,3,4,5,6

mean =  

median = 4, as number of observations is odd.

so, roadsters has greater median as well mean than bandits.

→option a is true about the repairs performed on 2 types of cars:

bandits have lower median and mean than roadsters.

(-5,-28)

i graphed to on desmos.