Hypothesis test for the differ

I am looking to understand the formula for calculating the standard deviation for the T Statistic – in the problem attached among learning th T Statistic.

Hypothesis test for the differ

Hypothesis test for the difference of population means: Paired comparisons
A personal computer manufacturer is interested in comparing assembly times for two keyboard assembly processes. Assembly times can vary considerably from worker to worker, and the company decides to eliminate this effect by selecting a random sample of 8 workers and timing each worker on each assembly process. Half of the workers are chosen at random to use Process 1 first, and the rest use Process 2 first. For each worker and each process, the assembly time (in minutes) is recorded, as shown in Table 1.

Worker Process 1 Process 2 Difference

1 79 61 18
2 64 60 4
3 68 50 18
4 77 71 6
5 48 25 23
6 62 42 20
7 87 84 3
8 74 65 9

Based on these data, can the company conclude, at the 0.10 level of significance, that the mean assembly times for the two processes differ? Answer this question by performing a hypothesis test. Perform a two-tailed test and answer the questions below.

Hypothesis test for the differ

Please see attached file for full problem.

Hypothesis test for the difference of population means: Z test
According to the historical data, the life expectancy in the United States is equal to the life expectancy in Japan. A new study has been made to see whether this has changed.

Hypothesis test for the differ

Attached is 2 slides on powerpoint. The 1st slide is the problem and the 2nd slide is the answer format. Answer 3 is completed because it requires the use of a t test with degree of freedom that equals 11.

Attached also is the excel data

Please help with 1,2,4,5 and 6 only

1) eg: u=0 or u>0 etc
2) same as 1
3) answered already
4) test statistic
5) criticlal value
6) Yes or No

The owner of a chain of mini-marktes wants to compare the saled performance of two her stores. Store 1 and Store 3. Though the two stores have been comparable in the past, the owner has made several improvements to Store 2 and wishes to see if the improvements have made store 2 more popular than store 1. sales can vary considerably depending on the day of the week and the season of the year, so she decides to elinimate such effects by making sure to record each stores’ sales on the same sample of days. After choosing a random sample of 12 days, she records the sales for each store on these days, as shown in table 1.
Based on these data, can the owner conclude, at the 0.01 level of significance, that the mean daily sales of store 2 exceeds that of store 1?