The local public transport authority is conducting research into commuter behaviour. A previous census indicated that the mean commuter time was 45 minutes with a standard deviation of 9.1 minutes. After some recent infrastructure upgrades and a new train timetable, the transport authority would like to test whether average commuter time has decreased. A random sample of 50 commuter times has been collected. 49.9
43.8
41
45.6
38.7
43.6
42.9
48
39.3
50.9
44.4
37.3
30.7
39.7
51.6
40.6
46.9
61.3
50.6
47.2
53
44
44.4
47.8
35.5
46.8
50.1
37.5
38.4
48.6
32.7
50.8
38.8
49
43.5
37.6
31
49.3
46.9
42.7
47.6
41.1
53.2
41.5
45.3
51.2
42.9
43.6
41.6
49.3
Conduct a hypothesis test to test whether the new changes have decreased mean commuter time.1) From the following options, select the correct null and alternate hypotheses for this test:A. H0: μ = 45, Ha: μ > 45B. H0: μ > 45, Ha: μ = 45C. H0: μ = 45, Ha: μ < 45D. H0: μ = 45, Ha: μ ≠ 45
2) Calculate the test statistic.
3) Calculate the test statistic.
4) Therefore, at a significance level of 0.05 the null hypothesis is rejectednot rejected.

and

The null hypothesis is not rejected

Step-by-step explanation:

Given

Random sample of 50 commuter times

Solving (a): The null and alternate hypothesis

From the question, a previous census shows that:

and

This is the null hypothesis i.e.

Reading further, a new test was to show whether the average has decreased.

This is the alternate hypothesis, and it is represented as:

Solving (b) and (c): The test statistic (T).

This is calculated using:

In this case:

  and

So:

Solving (c): Accept or reject null hypothesis

First calculate the degrees of freedom (df)

From the t distribution table,

At: ,   and

the t score is:

So, the null hypothesis is not rejected

d

step-by-step explanation:

d

the most boring thing ever written

step-by-step explanation:

i am writing something. yes, i plan to make it the most boring thing ever written. i go to the store. a car is parked. many cars are parked or moving. some are blue. some are tan. they have windows. in the store, there are items for sale. these include such things as soap, detergent, magazines, and lettuce. you can enhance your life with these products. soap can be used for bathing, be it in a bathtub or in a shower. apply the soap to your body and rinse. detergent is used to wash clothes. place your dirty clothes into a washing machine and add some detergent as directed on the box. select the appropriate settings on your washing machine and you should be ready to begin. magazines are stapled reading material made with glossy paper, and they cover a wide variety of topics, ranging from news and politics to business and stock market information. some magazines are concerned with more recreational topics, like sports card collecting or different kinds of hairstyles. lettuce is a vegetable.