Question

Pelican Stores market heavily to women in the 25 – 40-year age group. They consistently offer a mix of classic and contemporary apparel to attract shoppers in that age group. Use the Pelican Stores data to test whether the (population) mean age of a Pelican customer is less than 40. Test using a level of significance of α = 0.05.

Specify the random variable and distribution to be used in this hypothesis test.

Calculate the p-value Draw a graph and show the p-value
Show your work and any calculator functions used.

Compare the p-value with α   Decide to Reject or Fail to reject the null hypothesis      

Conclusion. State your results in non-technical terms.

32

36

32

28

34

44

30

40

46

36

48

40

40

46

24

36

22

40

32

56

28

38

50

42

48

60

54

42

32

70

28

52

44

34

56

36

42

50

44

58

42

46

48

54

38

60

46

30

32

46

38

68

78

20

32

38

54

48

46

50

46

30

54

42

48

62

34

28

46

54

30

32

22

32

74

62

42

28

38

54

68

30

36

44

44

62

48

36

20

42

54

54

72

30

46

44

30

52

30

44

Answer 1

Here claim is that mean is less than 40

$H_0:\mu=40$ vs $H_1:\mu<40$

Now for given sample $\overline{x}=AVERAGE(G7:G205)=43.08$ and standard deviation is $\sigma=STDEV(G7:G205)=12.389$

As sample size is sufficient large we will use z statistics

$z=\frac{\overline{x}-\mu}{\frac{\sigma }{\sqrt{n}}}=\frac{43.08-40}{\frac{12.389}{\sqrt{100}}}=2.49$

So P value is $P(z<2.49)=0.9936$

As P value is greater than alpha=0.05

WE fail to reject the null hypothesis

Hence we do not have sufficient evidence to support the claim that mean is less than 40