Chi square exercises of independence and goodness of fit

The structure of the development of the exercises is as follows: - Hypothesis. - Calculation of expected frequencies, if necessary. - Range table with signs (exercise 3). - Calculations necessary for statistics. - Statistical test. - Critical value or values. - Rejection region. - Conclusion.

Activities to develop

1) It is desired to test if the type of defect observed in the units produced in a manufacturing plant is related to the shift in which they are manufactured. A sample of products from the different shifts is taken and the results shown in the table are obtained:

	Type of deffect
turn	A	B	C	D	totals
morning	16	22	46	14	98
evening	27	32	35	6	100
night	34	18	50	21	123
totals	77	72	131	41	321

Perform the hypothesis test appropriate to the case using a 1% significance level and conclude.

2) 15 years ago, a certain company threw into its lake puye, pejerrey, catfish and trout in percentages of 20, 15, 40 and 25, respectively. Has the original distribution of fish changed over these 15 years, if a recent random sample provided the amounts shown in the table below? Use a 5% significance level and conclude.

crappie in the lake	puye	silverside fish	catfish	trout
number of fish	132	100	200	168

3) The following data corresponds to the operating hours of the last smartphone before needing to recharge the battery.

4.3

3.8

4.6

3.5

4.2

4.5

4.3

3.8

3.7

4.3

At the 5% level of significance, it tests the hypothesis that the latest smartphone runs for a median of 4.5 hours before requiring battery recharging. It concludes.

Please I need all the development of each exercise, with clear letters