Please, I need help with these questions

Answer them with R studio Programm if apply

1) A credit card company offers 13 different cards. An analyst randomly selects 800 credit card applications and counts the number of applications for each card.

Card Count

1 27

2 17

3 46

4 21

5 71

6 79

7 168

8 95

9 69

10 97

11 40

12 53

13 17

Are there any differences among the number of applications for various cards? We will use the Chi-Square Test.

a)State the null hypothesis

b)What is the expected number of applications per card under the null hypothesis?

c)Compute the statistic

d)What is the appropriate number of degrees of freedom?

e)Test the null hypothesis at the 0.01 level. What is the critical value of the chi-square statistic? What do you conclude?

f)Calculate the residual for each card. How many cards fall below the number of expected applications? How many above?

g) make a grouped barplot of the observed and expected frequencies.

2)

A marketing is expert is hired by a soap manufacturer. The manufacturer is trying to decide on which of four wrappings to use for their soap. To help make a decision, the soap is placed in the different wrappings and distributed to five different stores. After 2 weeks, the following number of soaps were sold:

Wrapping Number Sold

A 90

B 98

C 130

D 82

Is there a sufficient basis for the marketing expert to make a decision among wrappings? If so, which should be chosen? Use alpha=0.05.

3)

In Mendel's famous experiment with pea plants, he produced 315 yellow round phenotypes, 101 yellow wrinkled phenotypes, 108 green round phenotypes, and 32 green wrinkled phenotypes. Based on genetic theory, the ratio of yellow round to yellow wrinkled to green round to green wrinkled phenotypes is expected to be 9:3:3:1. Do the data conform to the expected distribution? Use a chi square.

a)State the null and alternative hypotheses.

b)What is the expected number of each phenotype?

c)What is the appropriate number of degrees of freedom?

d)Test the null hypothesis at the 0.05 level. What do you conclude? Interpret your results.

e) Make a grouped barplot of your observed and expected frequencies.