State whether the following statements are True or False. Give reason in support of your answer:

(i) The R- chart is suitable when subgroup size is greater than 10.

(ii) In single sampling plan, if we increase acceptance number then the OC curve will be steeper.

(iii) If the effect of summer and winter is not constant on the sale of AC then we use the additive model of the time series.

(iv) If a researcher wants to find the relationship between today’s unemployment and that of 5 years ago without considering what happens in between then the partial autocorrelation is the better way in comparison to autocorrelation.

(v) A system has four components connected in parallel configuration with
reliability 0.2, 0.4, 0.5, 0.8. To improve the reliability of the system most, we
have to replace the component which reliability is 0.2. 

) The marketing manager of a company recorded the number of mobiles sold quarterly for which are given in the following table:

Year	Quarter
2018		48	41	60	65
2019		58	52	68	74
2020		60	56	75	78

(i) Find the quarterly seasonal indexes for the mobile sold using the ratio to trend method.
(ii) Do seasonal forces significantly influence the sale of mobile? Comment.
(iii) Also find the deseasonalised values. 

A system has seven independent components and reliability block diagram of it shown as follows:

Find reliability of the system.

If a researcher wants to find the relationship between today’s unemployment and that of 5 years ago without considering what happens in between then the partial autocorrelation is the better way in comparison to autocorrelation.

The marketing manager of a company recorded the number of mobiles sold quarterly for which are given in the following table:

(i) Find the quarterly seasonal indexes for the mobile sold using the ratio to trend
method.
(ii) Do seasonal forces significantly influence the sale of mobile? Comment.
(iii) Also find the deseasonalised values. 

If the effect of summer and winter is not constant on the sale of AC then we use the additive model of the time series.

An office supply company ordered a lot of 400 printers. When the lot arrives the company inspector will randomly inspect 12 printers. If more than three printers in the sample are non-conforming, the lot will be rejected. If fewer than two printers are nonconforming, the lot will be accepted. Otherwise, a second sample of size 8 will be taken. Suppose the inspector finds two non-conforming printers in the first sample and two in the second sample. Also AQL and LTPD are 0.05 and 0.10 respectively. Let incoming quality be 4%.

(i) What is the probability of accepting the lot at the first sample?
(ii) What is the probability of accepting the lot at the second sample? 

Differentiate between the autoregressive and moving average models of time series.