A study claims that college students spend an average of 4 hours or less studying per day. A researcher wants to check if this claim is true. A random sample of 121 college students randomly selected and it showed that average of hours studying per day was 3.15 with a standard deviation of 1.2 hours. Using the 10% significance level, can you conclude that the claim college students spend an average of 4 hours or less studying per day is valid?
1. H0 hypothesis: A. μ > 4 B. μ ≥ 4 C.μ ≤ 4 D. μ < 4
2. Critical Value: A. -1.28 B. 1.28 C. 1.645 D. -1.645
3. Test statistics: A. -5.89 B. 5.89 C. -7.79 D. 7.79
4. Comment: A: Accept that college students spend an average of 4 hours or less studying per day
B:Reject that college students spend an average of 4 hours or less studying per day

Question

contestada

Respuesta :

wifilethbridge wifilethbridge · Answer 1 · 2019-08-08T08:09:33+02:00

Answer:

n = 121

x = 3.15

[tex]\sigma = 1.2[/tex]

Since we are given that the claim is college students spend an average of 4 hours or less studying per day is valid

Null hypothesis : [tex]H_0: \mu>4[/tex]

Alternate hypothesis: [tex]H_a:\mu\leq 4[/tex]

1) [tex]H_0: \mu>4[/tex]

Now we are given that significance level is 10%

So, confidence interval is 90%

Critical value at 90% is 1.645

2)Critical value : B : 1.645

Since n >30

So we will use z test

Now we are supped to calculate z statistics

Formula : [tex]z=\frac{x-\mu}{\frac{\sigma}{\sqrt{n}}}[/tex]

[tex]z=\frac{3.15-4}{\frac{1.2}{\sqrt{121}}}[/tex]

[tex]z=-7.79[/tex]

3)So, Test statistics: C. -7.79

Since the z value falls in the critical region

So, we reject the null hypothesis

So, that college students spend an average of 4 hours or less studying per day

4) A: Accept that college students spend an average of 4 hours or less studying per day