How do you position yourself when you are going to sleep? A website 5 tells us that \(41 \%\) of us start in the fetal position, another \(28 \%\) start on our side with legs straight, \(13 \%\) start on their back, and \(7 \%\) on their stomach. The remaining \(11 \%\) have no standard starting sleep position. If a random sample of 1000 people produces the frequencies in Table 7.11, should you doubt the proportions given in the article on the website? Show all details of the test, and use a \(5 \%\) significance level.

Table 7.11 Starting sleep positions

\begin{array}{lc}
\hline Sleep position & Frequency \\
\hline Fetal & 391 \\
Side, legs straight & 257 \\
Back & 156 \\
Stomach & 89 \\
None & 107 \\
\hline Total & 1000 \\
\hline
\end{array}