Question

In: Statistics and Probability

My co-worker alternates between driving herself to work and riding with her friend who lives nearby...

My co-worker alternates between driving herself to work and riding with her friend who lives nearby and works close to her. I will compare the mean time it takes for her to get to work each morning that she drives (which will be group 1) vs. when she rides with her friend (group 2). I believe the mean time it takes her to get to work when she drives herself (group 1) is less than the mean time it takes when she rides with her friend (group 2).

u1 = 20 mins (mean time – drives herself)

u2 = 30 mins (mean time – rides with friend)

s1 = 5 mins (standard deviation – drives herself)

s2 = 10 mins (standard deviation – rides with friend)

n1 = 20 days (sample days – drives herself)

n2 = 20 days (sample days – rides with friend)

I will construct a hypothesis test using a significance level of .05.

Please help with the answer with steps taken to get answer. Thank you!

Expert Solution

: mean time it takes her to get to work when she drives herself (group 1)

: mean time it takes when she rides with her friend (group 2)

Claim (Believe) : the mean time it takes her to get to work when she drives herself (group 1) is less than the mean time it takes when she rides with her friend (group 2). i.e < i.e -<0

Null hypothesis :H_o : - = 0

Alternate Hypothesis : H₁ : -<0 (Left tailed test)

Assumed population variances are not equal.

= 20 mins (mean time – drives herself)

= 30 mins (mean time – rides with friend)

s₁ = 5 mins (standard deviation – drives herself)

s₂ = 10 mins (standard deviation – rides with friend)

n₁ = 20 days (sample days – drives herself)

n₂ = 20 days (sample days – rides with friend)

For left tailed test :

As P-Value i.e. is less than Level of significance i.e (P-value:0.0002 < 0.05:Level of significance); Reject Null Hypothesis

There is Sufficient evidence to conclude that the mean time it takes her to get to work when she drives herself (group 1) is less than the mean time it takes when she rides with her friend (group 2).

orchestra answered 2 years ago

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