Question

Is there evidence that the mean annual salary of a Tesla owner is more than $253500? Data was collected from 36 Tesla owners across the US. The mean annual salary of those 36 Tesla owners was $254000 with a standard deviation of $1057.  Answer this question,  at the 1% significance level, by performing the following steps of a hypothesis test .

a) Complete the null and alternative hypotheses by typing into the box as indicated.

Ho : mu   (Type one:  <, =, >)    (type a value)
Ha : mu   (Type one:  <, =, >)    (type a value)

b)  Complete the probability statement for the probability of observing a mean salary at least as extreme as the one measured for this sample.

P( X_bar __(I)__ __(II)__ )

• Which symbol goes in blank (I)? Choose one:  <, =, >. Type the answer into this box.
• What number goes in blank (II)? Type the relevant number into this box.

c)  Complete the following sentence. For each box, choose an option and type its corresponding letter (A, B, etc...) into the box .

This test uses the  (A.  z B. t  C.  F) test statistic. Calculating this test statistic requires knowing the standard deviation of the  (A.  sample B.  population).

d) Calculate the test statistic. Type the value, rounded to 2 decimals, in the box.

Answer for (d):  

e) This figure represents the density curve of the test statistic. Answer the questions below about the distribution.

• What is the value of the test statistic at the center of the distribution? Type the number in the box.
  
  Answer:  
  
• Which shaded region or regions best represent the P-value for this test?   Choose an option from the list and type its letter (A, B, or C) in the box
  
  A. I B. II  C I and II
  
  Answer:  
  
• How many degrees of freedom are there for this distribution? Type the number in the box.
  
  Answer:   

f) Find an interval containing this test's P-value using one of the following tables:  normal table, t-table.  Type values for the lower and upper bounds, recorded to 4 decimals, into the correct boxes.

Answer for (f):   P-Value

g) Complete this concluding sentence. For each box, choose one of the two options and type its corresponding letter (A or B) into the box.

We  (A.  reject  B.  fail to reject) the null hypothesis. There (A.  is  B.  is no) evidence that the mean annual salary of a Tesla owner is (A.  less  B.  more) than $253500 at the 1% significance level. This refers to the (A.  sample  B.  population).

Answer 1

In case of a question with multiple sub-parts, we have the option to answer only first 4 sub-parts, thus I am here answering (a)-(d). If you want the solution to remaining ones, please post those as a new question.

a) Since we are to test whether the mean annual salary of a Tesla owner is MORE THAN $253500, thus, our null hypothesis will be

Ho: mu= 253500

and our alternative hypothesis will be

Ha: mu> 253500 (Right- tailed)

(b) Since for the sample data of 36 Tesla owners, the mean is $254000, our Probability statement will be

P(Xbar > 254000)

(c) Since we are to test the significance of a single mean and the sample standard deviation is given, we will use the t-statistic, thus option B. is correct. Further, t-statistic requires the knowledge of sample standard deviation, hence option A is correct.

(d) The t-statistic is given by

t= (xbar- mu)/ S/sqrt(n)

Given that xbar= 254000, mu= 253500, S=sample standard deviation= 1057 and n= sample size= 36

Hence t= (254000-253500)/1057/Sqrt(36)

=500/1057/6

= 3000/1057

=2.8382213813

= 2.84 (two decimal places)