statistic is about hypothesis testing (null hypothesis and alternative hypothesis)

statistic is about hypothesis testing (null hypothesis and alternative hypothesis)

Please use excels to solve Question 1. Please attach your answers in the word document as well as upload the original excel work sheet or workbook so that I can edit them if I need to.

Question 1:
According to research of a telephone company, an average time of phone call per household is 86 times in a month. There was a change in phone charge last month. According to most recent research on 100 households, an average time of phone call has decreased to 84 times a month, and its standard deviation is 12. Please verify whether it supports the statement “The reason for the decrease in times of phone call is due to change in phone charge”. Use level of significance 5% to test this hypothesis.

Hint: the answers calculated by hand are the following. This answer provided is for your reference to see if your work is correct or close when you calculate them on excel:

Hypothesis –  H0 : µ = 86
H1: µ < 86

n = 100     x¯   = 84     s = 12     a= 0.05

C x¯  = 86 – 1.645 × 12 / v 100 = 84.03

Critical Region  x¯   < 84.03

x¯ = 84 is included in the critical region (x¯   < 84.03)

Therefore; the null hypothesis is rejected and the alternative hypothesis is accepted.

The number of times the phone was used has decreased due to change in charge of the phone bill.

Please use excels to solve Question 2. Please attach your answers in the word document as well as upload the original excel work sheet or workbook so that I can edit them if I need to.

Question 2:
There is a factory that manufactures tire. The distance covered for the tire this factory manufactures is 25,000 km. This time they invented a tire with longer durability. 30 samples were selected for research, and the average sample mean was 25,500 km. The sample standard deviation is 1,700 km. Please verify the statement “The new version of tire has improved in durability” using level of significance 5% to test this hypothesis.
In addition to this question, please answer what will happen if the significance level is changed to 1%. Also in order to reject the null hypothesis, please calculate what  the greatest value of significance level should be (p value).

Hint: the answers calculated by hand are the following. This answer provided is for your reference to see if your work is correct or close when you calculate them on excel:

Hypothesis –  H0 : µ = 25,000
H1: µ > 25,000

n = 30     x¯   = 25,500    s = 1,700    a= 0.05

C x¯  = 25,000 + 1.699 (using t distribution, freedom is 30-1 = 29)  × 1,700 / v 30
= 25,527.3

Critical Region  x¯    > 25,527.3

x¯ = 25,500 is not included in the critical region (x¯    > 25,527.3)

Therefore; the null hypothesis is not rejected and the alternative hypothesis is not accepted.

The new version of tire has not improved in durability.

Please use excels to perform t-test for Question 3. Please attach your answers in the word document as well as upload the original excel work sheet or workbook so that I can edit them if I need to.

Question 3:
The percentage of supporter for B party who has voting rights in city A has been 32%.  In 1994, there was political change in government and wants to find out whether there was change in percentage of supporter for the party. The research was performed on sample of 200 people and the supporter average mean for the B party was 37%. The sample standard deviation was 48%. Please verify if party B’s support rate has increased significantly.

Hint: the answers calculated by hand are the following. This answer provided is for your reference to see if your work is correct or close when you calculate them on excel;however, this answer may or may not have performed t-test so please adjust your answer accordingly to t-test.
Hypothesis –  H0 : µ = 0.32
H1: µ > 0.32

n = 200    x¯   = 0.37    s = 0.48    a= 0.05

C x¯  = 0.32 + 1.645× 0.48 / v 200
= 0.376

Critical Region  x¯    > 25,527.3

x¯   = 0.37  is not included in the critical region

Therefore; the null hypothesis is not rejected and the alternative hypothesis is not accepted.

You can not say that party B’s support rate has increased significantly.

Please make sure that all answers are pasted on to word document as well as attach your excel file  (your excel sheet or excel workbook) so I can edit or refer to it. Please set up your excel worksheet so that I can print out the work on excel nicely on A4 paper. The printed out work of excel should be no more than 3 A4 papers. Make sure you label your work (which questions you are working on) on excel so I can find them easily according to questions.

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