A shoe manufacturer offers rock climbing shoes in black, blue, and pink. Of the first 1000 shoes sold, 400 were black. Calculate the value of the appropriate test statistic to determine if customers have a preference for black rock climbing shoes. Assume random sampling, variance homogeneity, and that preference is approximately normally distributed.
Try to solve this problem yourself before moving on to the solution below
.
.
.
.
.
.
We are testing the null hypothesis
\( H_0 : p = \frac{1}{3} \)
against the alternative hypothesis
\( H_a : p > \frac{1}{3} \)
The sample proportion
\( \hat{p} = \frac{400}{1000} = 0.4\)
for n=1000
The Z statistic can be calculated as:
\( Z = \frac{\hat{p} - p}{\sqrt{\frac{p(1-p)}{n}}} = \frac{0.40 - \frac{1}{3}}{\sqrt{\frac{\frac{1}{3}(1-\frac{1}{3})}{1000}}} \approx 4.47 \)
.
.
😃 Over to you: Were you able to solve this?
👉 If you liked this post, don’t forget to leave a like ❤️. It helps more people discover this newsletter on Substack and tells us that you appreciate solving these weekly questions. The button is located towards the bottom of this email.
👉 If you love reading this newsletter, feel free to share it with friends!
No posts
Comments
Nothing yet. Say the first thing.
Sign in to join the conversation.