Question

Question 1:

I believe that the population mean the amount of time millennials spend on social media. My findings consist of studying a group of 8 millennials for 24 hours.

Guest 1	3 hr
Guest 2	2 hr 38 min
Guest 3	2 hr 45 min
Guest 4	1 hr 52 min
Guest 5	2 hr 7 min
Guest 6	1 hr 39 min
Guest 7	3 hr 1 min
Guest 8	2 hr 17 min

I believe the population mean is less than 2.24

Question 2:

I am not certain that I am giving you the correct information so if not please let me know so I can get it correct so everyone can attempt to figure it out.

So I asked 8 people I work with how often they order for deliver to their home here are there answers

1-2

2-4

3-0

4-2

5-3

6-1

7-4

8-5

I will be using the .05 hypothesis significance level to compute my problem with a population mean.

Answer 1

Q1.

Sample-i	Time	Time in hrs. (x_i)	(x_i - x̄)^2
1	3 hr	3.000	0.343
2	2 hr 38 min	2.633	0.048
3	2 hr 45 min	2.750	0.113
4	1 hr 52 min	1.867	0.300
5	2 hr 7 min	2.117	0.089
6	1 hr 39 min	1.650	0.585
7	3 hr 1 min	3.017	0.363
8	2 hr 17 min	2.283	0.017
	Totals	19.317	1.856
	Denominator	8	7
	Totals / Denominator	2.415	0.265
		Sample mean (x̄)	Sample var (s^2)

So, sample-based information is as follows:

Sample mean (x̄) = 2.415
Sample stdev (s) = sqrt(0.265) = 0.515
Sample size (n) = 8

Null hypothesis (H0): Population mean >= 2.24
Alternate hypothesis (H1): Population mean < 2.24 [Your belief]

Note that the number of samples (n) is only 8 which is < 30 and also the population standard deviation is unknown. So, we have to use the t-distribution to compute the test statistic.

So,

Test statistic, t_stat = (x̄ - 2.24) / (s / √n) = (2.415 - 2.24) / (0.515/√8) = 0.9611

The critical value, t_crit will be negative (-1.89) as it is a left-tailed test.

So, t_stat > t_crit for a left-tailed test and hence the null hypothesis cannot be rejected. So, your claim cannot be statistically validated with the given sample information.

Q2.

One needs to provide the target value (i.e. the claim) for the population mean to conduct the test.